Lesson Plans to Introduce the Graphing Linear Equations …€¦ · Lesson Plans to Introduce the...
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Lesson Plans to Introduce
the Graphing Linear Equations Unit
Susan Mercer
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1) Introducing the pattern.
❐ Hand out a piece of graph paper to each student.
❐ Put the transparency of pattern #1 on the overhead. Show only steps 0 and 1,
cover the rest with a paper.
❐ Ask students to describe what they see: how many squares do you see in the
pattern step 0? how many squares do you see in the pattern step 1?
❐ Ask students what do they think comes next: what do you think step 2 will look
like? how many squares will you need?
❐ Uncover step 2.
❐ Ask students what do they think comes next: what do you think step 3 will look
like? how many squares will you need?
❐ Uncover step 3.
❐ Ask students what do they think comes next: what do you think step 4 will look
like? how many squares will you need?
❐ Uncover step 4.
❐ Tell students to copy the pattern on their graph paper, clearly labeling each step.
❐ Ask students to describe the pattern: what do you notice about the pattern?
does it go up or down? how many squares do you need to add each time? are the
number of squares odd or even?
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2) Creating a table.
❐ Put the table #1 transparency on the overhead and ask students to copy it on
their graph paper.
❐ Tell students that step 0 is where the pattern starts.
❐ Have students complete the table based on the pattern and the number of
squares.
❐ Ask different students to give you the number of squares they wrote down for
each step and complete the table on the overhead. This will provide students
with immediate feed back.
❐ Ask students for patterns they notice on the table: what do you notice about the
numbers on the table? is there a pattern? how many squares would you have on
step 5? how do you know?
❐ Based on the students’ responses extend the table to steps 5, 6 and 7.
❐ Tell students to write the increment of squares from one step to the next.
❐ The finished table should look like this:
step number of squares
0
1
2
3
4
5
6
7
3
5
7
9
11
13
15
17
+2
+2
+2
+2
+2
+2
+2
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3) Graphing the pattern
❐ On the same graph paper students draw a graph. Show students how to do a
graph by drawing the x axis, then the y axis and label each one using a scale of
one. Make sure they label the origin.
❐ Show students how to plot ordered pairs. Show them where zero step is and ask:
how many squares are in the pattern in step 0? students can use the table or
the pattern to answer. Mark the ordered pair on the overhead graph and
students plot it on their graphs. Repeat this modeling process for steps 1, 2 and
3.
❐ Next, ask: what do you notice about the first four points you plotted? students
may respond that the points are in a straight line or evenly distributed. These
observations are very important.
❐ Ask students: can you plot step 4, 5, 6 or 7? why not?
❐ Ask students to connect the ordered pairs with a straight line, using a ruler.
❐ Ask students: can you identify on the graph the +2 from the table? Show
students how to label the +2 on the graph.
❐ Each student should have the following graph.
+2
+2+2
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4) Introduction to vocabulary words
❐ Ask students: how many squares did you add from one step to another?
❐ Tell the students that the number of squares you add from one step to another is
called the SLOPE.
❐ Ask students to identify the slope on the table and the graph and and model how
to label it on the overhead.
❐ Students identify and label SLOPE on their pattern, the table and the graph.
❐ Ask students: how many squares did the pattern start with?
❐ Tell the students that the number of squares the pattern started with is called
the Y-INTERCEPT.
❐ Ask students to identify the y-intercept on the table and the graph and model
how to label it on the overhead.
❐ Students identify and label Y-INTERCEPT on their pattern, the table and the
graph.
5) Writing equations
❐ Using the slope and the y-intercept, model for the students how to write the
equation for the pattern (y=slope x + y-intercept).
❐ Explain to the students that the equation describes the pattern using numbers
and can be used to calculate the number of squares that a specific step will have.
For example: step 10 or step 1000)
6) When you finish introducing pattern #1, repeat steps 1 to 5 for pattern #2.
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At the end of Pattern #1 students’ page should look as follows:
0 1 2 3 4
+2+2
+2+2
slope
slope
y-intercept
y-intercept
Patterns and Graphing
Pattern #1
Nameperdate
Equation: y = 2 x + 3
step
pattern
+2
+2+2
y-intercept
step number of squares
0
1
2
3
4
5
6
7
3
5
7
9
11
13
15
17
+2
+2
+2
+2
+2
+2
+2
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At the end of Pattern #2 students’ page should look as follows:
step number of squares
0
1
2
3
4
5
6
7
9
8
7
6
5
4
3
2
–1
–1
–1
–1
–1
–1
–1
–1 –1–1 –1
slope
slope
y-intercept
y-interceptPatterns and Graphing
Pattern #2
Nameperdate
Equation: y = –1 x + 9
step
pattern
0 1 2 3 4
–1–1
–19
slope
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Teacher’s notes: Connecting the pattern, the table, the graph and the equation.
✏ Slope: the steepness of the line;
On the pattern, the slope is the number of squares you add or subtract to obtain the
next step;
On the table, the slope is the number you add or subtract from the previous step to
obtain the next step;
On the graph, you can recognize the slope by observing how many squares you have
to go up for every one that you go across.
0 1 2 3 4
+2+2
+2+2
slope
step number of squares
0
1
2
3
4
5
6
7
3
5
7
9
11
13
15
17
+2
+2
+2
+2
+2
+2
+2
+2
+2+2
Equation: y = 2 x + 3
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Teacher’s notes: Connecting the pattern, the table, the graph and the equation. (cont)
✏ y-intercept: the value of y when x=0;
On the pattern, the y-intercept is the number of squares for step 0;
On the table, the y-intercept is the number of squares for step 0;
On the graph, the y-intercept is where the line crosses the y-axes.
0 1 2 3 4
y-intercept
step number of squares
0
1
2
3
4
5
6
7
3
5
7
9
11
13
15
17
Equation: y = 2 x + 3
3
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Teacher’s notes: Connecting the pattern, the table, the graph and the equation. (cont)
✏ linear or non linear: the graph is a straight line;
On the pattern, you always add or subtract the same number of squares;
On the table, you always add or subtract the same number from step to step;
On the graph, you can observe a straight line.
✏ ascending: the graph is a straight line going up;
On the pattern, you always add the same number of squares;
On the table, you always add the same number from step to step;
On the graph, you can observe a straight line going up;
Slope is positive.
✏ descending: the graph is a straight line going down;
On the pattern, you always subtract the same number of squares;
On the table, you always subtract the same number from step to step;
On the graph, you can observe a straight line going down;
Slope is negative.
✏ horizontal: the graph is a straight line that does not go up or down;
On the pattern, you add zero squares from one step to another;
On the table, you add zero from step to step;
On the graph, you can observe a horizontal line;
Slope is zero.
✏ equation: a numerical description of the pattern given by Y = slope X + y-intercept
the x is the step in the pattern;
the y is the number of squares in the pattern for step x;
slope is the number of squares we add or subtract from one step to another;
y-intercept is how many squares you start with.
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Transparencies
Pattern #1
0 1 2 3 4
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Table #1
step number of squares
0
1
2
3
4
5
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Graph #1
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Pattern #2
0 1 2 3 4
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IntroducingGraphing
Linear Equations
Susan Mercer
Answer Key
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Graphing Patterns
1) Study and complete the pattern.2) Complete the table.3) Label the X and Y axes and graph the pattern.4) Answer the questions.
0 1 2 3 4 5+1 +1+1+1+1
+2
+2+2
+2+2
y-intercept
+1
+1
+1
+1
+1
step number of squares
0
1
2
3
4
5
1
3
5
7
9
11
+2
+2
+2
+2
+2
+2
+1
What is the slope? ____2______ Show the slope on the pattern, table and graph.
What is the y-intercept? ___1___ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: ______y = 2x + 1__
Is the pattern linear or non-linear? ____linear___
Is the pattern ascending, descending, or horizontal? _______ascending_____
© Introducing Graphing Linear Equations ANSWER KEY page 1
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Graphing Patterns1) Study and complete the pattern.2) Complete the table.3) Label the X and Y axes and graph the pattern.4) Answer the questions.
+0
0 1 2 3 4 5
+0+0+0+0
+1 +1 +1 +1 +1
+1
+1
+1
+1
+1
step number of squares
0
1
2
3
4
5
3
3
3
3
3
3
+0
+0
+0
+0
+0
y-intercept
What is the slope? ___0________ Show the slope on the pattern, table and graph.
What is the y-intercept? ___3____ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: ____y = 0x + 3__________
Is the pattern linear or non-linear? ______linear_____
Is the pattern ascending, descending, or horizontal? ___horizontal__
© Introducing Graphing Linear Equations ANSWER KEY page 2
Key Question:
How is this problem different from the previous one?
You are not adding squares from one step to the next.
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Graphing Patterns1) Study and complete the pattern.2) Complete the table.3) Label the X and Y axes and graph the pattern.4) Answer the questions.
0 1 2 3 4 5
-2-2
-2-2
-2
+1 +1+1+1+1
+1
-2
+1
+1
+1
+1
+1
step number of squares
0
1
2
3
4
5
10
8
6
4
2
0
-2
-2
-2
-2
-2
Y-intercept
What is the slope? _______-2__ Show the slope on the pattern, table and graph.
What is the y-intercept? __10___ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: ____y = -2x + 10______
Is the pattern linear or non-linear? ___linear_________
Is the pattern ascending, descending, or horizontal? __descending___
© Introducing Graphing Linear Equations ANSWER KEY page 3
Key Question:
How is this problem different from the previous one?
You are taking away squares from one step to the next.
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Graphing Patterns1) Study and complete the pattern.2) Complete the table.3) Label the X and Y axes and graph the pattern.4) Answer the questions.
-4
+10 1 2 3 4 5+1 +1+1 +1
-4 -4
+4+4
y-intercept
+1
+1
+1
+1
+1
step number of squares
0
1
2
3
4
5
6
2
6
2
6
2
-4
+4
-4
+4
-4
Can you determine a slope? __no___Why or why not?__not a line_________
What is the y-intercept? _6_____ Show the y-intercept on the table, graph and rule.
Is the pattern linear or non-linear? _____non-linear________
Is the pattern ascending, descending, or horizontal? ___none____
© Introducing Graphing Linear Equations ANSWER KEY page 4
Key Question:
How is this problem different from the previous one?
Fisrt you take away four squares and next you add four squares.
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Graphing Number Patterns
1) Study and complete the pattern.2) Complete the table for x = 0, 1, 2, 3, 4, and 5.3) Label the X and Y axes and graph the pattern.4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 2, 5, 8, 11, _14, _17 _20, _23, _26_,
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
2
5
8
11
14
17
+3
+3
+3
+3
+3
+3
+1
What is the slope? ____3______ Show the slope on the table and graph.
What is the y-intercept? _2_____ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: ______y = 3x + 2___
Use the equation to find the value of y when x = 10? ____32_____Use the equation to find the value of y when x = 100? ____302______Use the equation to find the value of y when x = 1000? ___3002______
Is the pattern linear or non-linear? ___linear________
Is the pattern ascending, descending, or horizontal? ___ascending__
© Introducing Graphing Linear Equations ANSWER KEY page 5
Key Question:
How is this problem different from the previous one?
Insted of a picture you have numbers. The X is the step while the Y is the number of squares in the picture.
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Graphing Number Patterns1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 9, 8, 7, 6, 5, _4_, _3_, _2_, _1__,
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
9
8
7
6
5
4
-1
-1
-1
-1
-1
-1+1
What is the slope? ____-1____ Show the slope on the table and graph.
What is the y-intercept? ___9___ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: ____y = -1x + 9_______
Use the equation to find the value of y when x = 10? ____-19______Use the equation to find the value of y when x = 100? ____-100 + 9_= -91________Use the equation to find the value of y when x = 1000? ____-1000 + 9_= -991_____
Is the pattern linear or non-linear? _____linear_____
Is the pattern ascending, descending, or horizontal? ___descending__
© Introducing Graphing Linear Equations ANSWER KEY page 6
Key Question:
How is this problem different from the previous one?
The Y numbers are going down by one.
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Graphing Number Patterns
1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 6, 6, 6, 6, 6, _6_, _6_, _6_, _6_,
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
6
6
6
6
6
6
+0
+0
+0
+0
+0
What is the slope? ____0_____ Show the slope on the table and graph.
What is the y-intercept? ___6___ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____y = 0x + 6_______
Use the equation to find the value of y when x = 10? ______6______Use the equation to find the value of y when x = 100? ______6______Use the equation to find the value of y when x = 1000? ______6______
Is the pattern linear or non-linear? ____linear_______
Is the pattern ascending, descending, or horizontal? ___horizontal____
© Introducing Graphing Linear Equations ANSWER KEY page 7
Key Question:
How is this problem different from the previous one?
The Y numbers are always the same.
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Graphing Number Patterns
1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 0, 1, 2, 3, 4, _5_, _6_, _7_, _8__,
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
0
1
2
3
4
5
+1
+1
+1
+1
+1
+1+1
What is the slope? ____1_____ Show the slope on the table and graph.
What is the y-intercept? ___0___ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____y = 1x + 0______
Use the equation to find the value of y when x = 10? _____10______Use the equation to find the value of y when x = 100? _____100_____Use the equation to find the value of y when x = 1000? _____1000____
Is the pattern linear or non-linear? ___linear________
Is the pattern ascending, descending, or horizontal? __ascending__
© Introducing Graphing Linear Equations ANSWER KEY page 8
Key Question:
How is this problem different from the previous one?
The X and Y numbers are the same. You add one to each one.
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Graphing Equations
1) Study the equation y = 3x + 1
2) Looking at the equation, what is the slope? __3__
what is the y-intercept? __1___
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
1
4
7
10
13
16
+3
+3
+3
+3
+3
+1
+3
Show the slope on the table and graph. Is this the same as your answer in #2? __3__
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _1
Is the pattern linear or non-linear? __linear__________
Is the pattern ascending, descending, or horizontal? _ascending_
© Introducing Graphing Linear Equations ANSWER KEY page 9
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Graphing Equations
1) Study the equation y = 2x + 3
2) Looking at the equation, what is the slope? __2__
what is the y-intercept? __3___
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
3
5
7
911
13
+2
+2
+2
+2
+2
+1
+2
Show the slope on the table and graph. Is this the same as your answer in #2? _2___
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _3_
Is the pattern linear or non-linear? ___linear_________
Is the pattern ascending, descending, or horizontal? _ascending___
© Introducing Graphing Linear Equations ANSWER KEY page 10
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Graphing Equations
1) Study the equation y = –2x + 8
2) Looking at the equation, what is the slope? __-2_
what is the y-intercept? __8___
3) Complete the table for x = 0, 1, 2, 3, 4 and.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
8
6
4
20
-2
-2
-2
-2
-2
-2
+1
-2
Show the slope on the table and graph. Is this the same as your answer in #2? __-2_
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _8_
Is the pattern linear or non-linear? ___linear_______
Is the pattern ascending, descending, or horizontal? __descending_
© Introducing Graphing Linear Equations ANSWER KEY page 11
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Graphing Equations
1) Study the equation y = –1x + 7
2) Looking at the equation, what is the slope? _-1__
what is the y-intercept? __7___
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
+1
x y0
1
2
3
4
5
7
6
5
43
2
-1
-1
-1
-1
-1
+1-1
Show the slope on the table and graph. Is this the same as your answer in #2? _-1___
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _7
Is the pattern linear or non-linear? ____linear______
Is the pattern ascending, descending, or horizontal? __descending__
© Introducing Graphing Linear Equations ANSWER KEY page 12
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Graphing Equations
1) Study the equation y = x
2) Looking at the equation, what is the slope? __1__
what is the y-intercept? __0___
what is this type of equation called? __identity_
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
x y0
1
2
3
4
5
0
1
2
34
5+1
+1
+1
+1
+1
+1
+1+1
10100
10100
Show the slope on the table and graph. Is this the same as your answer in #2? __1__
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _0_
Is the pattern linear or non-linear? ____linear_______
Is the pattern ascending, descending, or horizontal? __ascending__
© Introducing Graphing Linear Equations ANSWER KEY page 13
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Graphing Equations
1) Study the equation y = 3x + –6
2) Looking at the equation, what is the slope? __3__
what is the y-intercept? __-6__
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
x y0
1
2
3
4
5
-6
-3
0
36
9+1
+3
+3
+3
+3
+3
+1
+3
10100
24294
Show the slope on the table and graph. Is this the same as your answer in #2? __3__
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _-6_
Is the pattern linear or non-linear? ___linear_______
Is the pattern ascending, descending, or horizontal? ___ascending___
© Introducing Graphing Linear Equations ANSWER KEY page 14
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Graphing Equations
1) Study the equation y = 3
2) Looking at the equation, what is the slope? __0___
what is the y-intercept? __3___
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
y-intercept
+1
+1
+1
+1
x y0
1
2
3
4
5
3
3
3
33
3+1
+0
+0
+0
+0
+0
10100
33
Show the slope on the table and graph. Is this the same as your answer in #2? __0__
Show the y-intercept on the table and graph. Is this the same as your answer in #2? _3_
Is the pattern linear or non-linear? ____linear_______
Is the pattern ascending, descending, or horizontal? _horizontal_
© Introducing Graphing Linear Equations ANSWER KEY page 15
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Family of Lines
1) Study the equation y = 2x + 1 what is the slope? __2__
what is the y-intercept? __1___
2) Study the equation y = 2x + 3 what is the slope? __2__
what is the y-intercept? __3__
3) Study the equation y = 2x what is the slope? __2__
what is the y-intercept? __0__
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
11+2
1
3
5
79
+2
+2
+2
+2
x y x y x y+1
+1
+1
+1
0
1
2
3
4
5+1
+1
+1
+1
+1
0
1
2
3
4
5+1
13+2
3
5
7
911
+2
+2
+2
+2
10+2
0
2
4
68
+2
+2
+2
+2
y-intercept y-intercept
© Introducing Graphing Linear Equations ANSWER KEY page 16
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y
x
+1
+1+2
+2
What do you notice about the three lines? ________parallel__________
What do the equations of the lines have in common? ________the slope__________
© Introducing Graphing Linear Equations ANSWER KEY page 17
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Family of Lines
1) Study the equation y = x + 2 what is the slope? __1__
what is the y-intercept? __2___
2) Study the equation y = x + 5 what is the slope? __1__
what is the y-intercept? __5___
3) Study the equation y = x + – 3 what is the slope? __1__
what is the y-intercept? __-3__
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
7+1
2
3
4
56
+1
+1
+1
+1
x y x y x y+1
+1
+1
+1
0
1
2
3
4
5+1
+1
+1
+1
+1
0
1
2
3
4
5+1
10+1
5
6
7
8
9
+1
+1
+1
+1
2+1
-3
-2
-1
0
1
+1
+1
+1
+1
y-intercept y-intercept
© Introducing Graphing Linear Equations ANSWER KEY page 18
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y
x
+1
+1+1
+1
+1+1
What do you notice about the three lines? ____________parrallel________
What do the equations of the lines have in common? _______slope__________
© Introducing Graphing Linear Equations ANSWER KEY page 19
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Family of Lines
1) Study the equation y = x + 2 what is the slope? __1__
what is the y-intercept? ___2__
2) Study the equation y = 3x + 2 what is the slope? __3__
what is the y-intercept? __2___
3) Study the equation y = –2x + 2 what is the slope? __-2_
what is the y-intercept? __2___
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
7+1
2
3
4
56
+1
+1
+1
+1
x y x y x y+1
+1
+1
+1
0
1
2
3
4
5+1
+1
+1
+1
+1
0
1
2
3
4
5+1
17+3
2
5
8
11
14
+3
+3
+3
+3
-8-2
2
0
-2
-4
-6
-2
-2
-2
-2
y-intercept y-intercept
© Introducing Graphing Linear Equations ANSWER KEY page 20
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y
x
+1
+1+1
+3
-2+1
What do you notice about the three lines? ____same y-intercept________
What do the equations of the lines have in common? _______y-intercept_______
© Introducing Graphing Linear Equations ANSWER KEY page 21
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Family of Lines
1) Study the equation y = 5 what is the slope? __0__
what is the y-intercept? ___5__
2) Study the equation y = 2 what is the slope? __0__
what is the y-intercept? __2___
3) Study the equation y = –3 what is the slope? __0__
what is the y-intercept? __-3__
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
5+0
5
5
5
55
+0
+0
+0
+0
x y x y x y+1
+1
+1
+1
0
1
2
3
4
5+1
+1
+1
+1
+1
0
1
2
3
4
5+1
2+0
2
2
2
2
2
+0
+0
+0
+0
-3-0
-3
-3
-3
-3
-3
-0
-0
-0
-0
y-intercept y-intercept
© Introducing Graphing Linear Equations ANSWER KEY page 22
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y
x
What do you notice about the three lines? ______they are horizontal_______
What do the equations of the lines have in common? ______slope_________
© Introducing Graphing Linear Equations ANSWER KEY page 23
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (3, 2).
2) Use the ruler to draw a line through the point (3, 2) with a slope of 2.
x yy-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
6+2
-4
-2
0
2
4
+2
+2
+2
+2
+1
+2( 3,2)
3) Looking at the graph, what is the y-intercept? __-4__
what is the equation of the line? __y = 2x - 4__
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? ___linear______
6) Is the pattern ascending, descending, or horizontal? __ascending__.
© Introducing Graphing Linear Equations ANSWER KEY page 24
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (2,1).
2) Use the ruler to draw a line through the point (2,1) with a slope of –2.
x yy-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
-5-2
5
3
1
-1
-3
-2
-2
-2
-2
+1
-2( 2,1)
3) Looking at the graph, what is the y-intercept? __5___
what is the equation of the line? __y = -2x + 5___
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? ___linear______
6) Is the pattern ascending, descending, or horizontal? __descending__.
© Introducing Graphing Linear Equations ANSWER KEY page 25
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (3, 5).
2) Use the ruler to draw a line through the point (3, 5) with a slope of 0.
x yy-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
5+0
5
5
5
5
5
+0
+0
+0
+0
( 3,5)
3) Looking at the graph, what is the y-intercept? __5___
what is the equation of the line? __y = 0x + 5___
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? ___linear______
6) Is the pattern ascending, descending, or horizontal? ___horizontal__.
© Introducing Graphing Linear Equations ANSWER KEY page 26
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (1, 3).
2) Use the ruler to draw a line through the point (1, 3) with a slope of –1.
x yy-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
-1-1
4
3
2
1
0
-1
-1
-1
-1
( 1,3)
-1+1
3) Looking at the graph, what is the y-intercept? __4___
what is the equation of the line? __y = -1x + 4_
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? ____linear____
6) Is the pattern ascending, descending, or horizontal? __descending__.
© Introducing Graphing Linear Equations ANSWER KEY page 27
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Finding the Equation of a Line
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
11+2
1
3
5
7
9
+2
+2
+2
+2
x y
+2+1
1) Study the graph.
2) Looking at the graph, what is the slope? __2__
what is the y-intercept? __1__
what is the equation of the line? __y = 2x + 1__
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? ___linear___
5) Is the pattern ascending, descending, or horizontal? __ascending__.
© Introducing Graphing Linear Equations ANSWER KEY page 28
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Finding the Equation of a Line
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
0-1
5
4
3
2
1
-1
-1
-1
-1
x y
-1+1
1) Study the graph.
2) Looking at the graph, what is the slope? __-1_
what is the y-intercept? __5__
what is the equation of the line? __y = -1x + 5__
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? ___linear___
5) Is the pattern ascending, descending, or horizontal? __descending__.
© Introducing Graphing Linear Equations ANSWER KEY page 29
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Finding the Equation of a Line
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
7+0
7
7
7
7
7
+0
+0
+0
+0
x y
1) Study the graph.
2) Looking at the graph, what is the slope? __0__
what is the y-intercept? __7___
what is the equation of the line? __y = 0x + 7_
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? ____linear____
5) Is the pattern ascending, descending, or horizontal? __horizontal__.
© Introducing Graphing Linear Equations ANSWER KEY page 30
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Finding the Equation of a Line
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
2+1
-3
-2
-1
0
1
+1
+1
+1
+1
x y
+1+1
1) Study the graph.
2) Looking at the graph, what is the slope? __1__
what is the y-intercept? __-3__
what is the equation of the line? __y = 1x - 3__
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? ____linear____
5) Is the pattern ascending, descending, or horizontal? ___ascending___.
© Introducing Graphing Linear Equations ANSWER KEY page 31
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Finding the Equation of a Line
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
-3-2
7
5
3
1
-1
-2
-2
-2
-2
x y
-2
+1
1) Study the graph.
2) Looking at the graph, what is the slope? __-2 _
what is the y-intercept? __7___
what is the equation of the line? __y = -2x + 7_
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? ___linear____
5) Is the pattern ascending, descending, or horizontal? __descending__.
© Introducing Graphing Linear Equations ANSWER KEY page 32
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Word Problem
Sabrina wants to buy a CD player. She has $2. She decides to save $3 from her allowance every week.
1) Complete a table and graph Sabrina’s savings during 10 weeks.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
17+3
2
5
8
11
14
+3
+3
+3
+3
Number of weeks
(X)
Sabrina’s savings
(Y)
y
x+1
+1
+1
+16
7
8
9
10+1
32+3
2023
26
29
+3
+3
+3+3
+3
+1
2) What is the slope? 3
3) What part of the word problem gives you the “slope”? amount added to the savings
4) What is the y-intercept? 2
5) What part of the word problem gives you the “y-intercept”? amount of money she had before the first week
6) What is the equation that represents Sabrina’s savings? y = 3x + 2
7) What does the X-axis represent? weeks
8) What does the Y-axis represent? money in savings
© Introducing Graphing Linear Equations ANSWER KEY page 33
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Word Problem
Sabrina has $12 saved. She decides to spend $2 a week on candy.
1) Complete a table and graph Sabrina’s savings during 10 weeks.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
2-2
12
10
8
6
4
-2
-2
-2
-2
Number of weeks
(X)
Sabrina’s savings
(Y)-2
+1
y
xout of money
+1
+1
+1
+16
7
8
9
10+1
-8-2
0
-2
-4
-6
-2-2
-2
-2
2) What is the slope? -2
3) What part of the word problem gives you the “slope”? how much she spenteach week
4) What is the y-intercept? 12
5) What part of the word problem gives you the “y-intercept”? amount of money she
started with
6) What is the equation that represents Sabrina’s savings? y = -2x + 12
7) During what week did Sabrina run out of money? Label it on the graph. 6
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Word Problem
Sabrina wants to buy a CD player. She has no money. She decides to save $2 from her allowance every week.
1) Complete a table and on graph paper graph Sabrina’s savings during 10 weeks.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
10+2
0
2
4
6
8
+2
+2
+2
+2
Number of weeks
(X)
Sabrina’s savings
(Y)
y
x+1
+1
+1
+16
7
8
9
10+1
1214
16
+2
+2
20+2
18+2+2
+2
+1
2) What is the slope? 2
3) What part of the word problem gives you the “slope”? amount added to savings per week
4) What is the y-intercept? 0
5) What part of the word problem gives you the “y-intercept”? amount of money she started with
6) What is the equation that represents Sabrina’s savings? y = 2x + 0
7) What does the X-axis represent? number of weeks
8) What does the Y-axis represent? amount of money in savings
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Graphing Linear Systems of Equations
A) Sabrina has $30 and she receives an allowance of $5 per week.
B) Sergio has $10 and he receives an allowance of $10 per week.
1) Complete a t-table and graph Sabrina and Sergio’s savings for 10 weeks.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
55+5
30
35
40
4550
+5
+5
+5
+5
+1
+1
+1
+16
7
8
9
10+1
6065
70
+5
+5
80+5
75+5
+5
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? __5__
What is the y-intercept? _30_
What is the slope? _10_
What is the y-intercept? _10_
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
60+10
10
20
30
4050
+10
+10
+10
+10
+1
+1
+1
+16
7
8
9
10+1
7080
90
+10
+10
110 +10100
+10+10
same amount of money
Sabrina has more money these weeks
2) Graph Sabrina and Sergio’s savings for 10 weeks.
3) What part of problem gives you the “slope”? amount of money added
4) What part of the word problem gives you the “y-intercept”? amount of money they start with
5) What is the equation that represents Sabrina’s savings? y = 5x + 30
6) What is the equation that represents Sergio’s savings? y = 10x + 10
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y
x5
1 2 3 4 5
1510
2520
Sabrina
Sergio
same amount of money
Sabrina has more money these weeks
During what week will Sabrina and Sergio’s savings be the same? ___4_____
Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
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Graphing Linear Systems of Equations
A) Sabrina has $ 15 and she receives an allowance of $ 5 per week.
B) Sergio has $ 30 and he receives an allowance of $ 2 per week.
1) Complete a t-table and graph Sabrina and Sergio’s savings for 10 weeks.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
40+5
15
20
25
30
35
+5
+5
+5
+5
+1
+1
+1
+16
7
8
9
10+1
4550
55
+5
+5
65+5
60+5
+5
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? __5__
What is the y-intercept? _15_
What is the slope? _2_
What is the y-intercept? _30_
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
40+2
30
32
34
3638
+2
+2
+2
+2
+1
+1
+1
+16
7
8
9
10+1
4244
46
+2
+2
50 +248
+2
+2
same amount of money
Sabrina has more money these weeks
2) Graph Sabrina and Sergio’s savings for 10 weeks.
3) What part of problem gives you the “slope”? amount of money added each week
4) What part of the word problem gives you the “y-intercept”? money that starts in the savings
5) What is the equation that represents Sabrina’s savings? y = 5x + 15
6) What is the equation that represents Sergio’s savings? y = 2x + 30
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y
x1 2 3 4 5
Sabrina
Sergio
same amount of money
Sabrina has more money these weeks
108642
During what week will Sabrina and Sergio’s savings be the same? ___5_____
Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
© Introducing Graphing Linear Equations ANSWER KEY page 39
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Graphing Linear Systems of Equations
A) Sabrina has saved $ 70 and spends $ 5 per week.
B) Sergio has saved $ 60 and spends $ 3 per week.
1) Complete a t-table and graph Sabrina and Sergio’s spending until they run out of money.
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
45-5
70
65
60
55
50
-5
-5
-5
-5
+1
+1
+1
+16
7
8
9
10+1
4035
30
-5
-5
20-5
25-5
-5
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? _-5__
What is the y-intercept? _70_
What is the slope? _-2_
What is the y-intercept? _60_
y-intercept
+1
+1
+1
+1
0
1
2
3
4
5+1
45-3
60
57
54
5148
-3
-3
-3
-3
+1
+1
+1
+16
7
8
9
10+1
4239
36
-3
-3
30-3
33-3
-3
same amount of money
Sabrina has more money these weeks
2) Graph Sabrina and Sergio’s spending.
3) What part of problem gives you the “slope”? the amount of money spent each week
4) What part of the word problem gives you the “y-intercept”? the amout of money that started in the savings
5) What is the equation that represents Sabrina’s savings? y = -5x + 70
6) What is the equation that represents Sergio’s savings? y = -3 + 60
© Introducing Graphing Linear Equations ANSWER KEY page 40
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y
x1 2 3 4 5
Sabrina
Sergio
same amount of money
Sabrina has more money these weeks
10
25
20
15
5
During what week will Sabrina and Sergio’s have the same amount of money?
___5___ Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
© Introducing Graphing Linear Equations ANSWER KEY page 41
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Unit Summary
Using words, graphs, diagrams and examples, clearly explain each one
of the following mathematical terms:
❒ pattern
❒ slope
❒ y-intercept
❒ equation
❒ linear
❒ non-linear
❒ ascending
❒ descending
❒ horizontal
© Introducing Graphing Linear Equations ANSWER KEY page 42
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Unit Summary Continue
© Introducing Graphing Linear Equations ANSWER KEY page 43
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Name: ____________________
Period: ________
Date: ______________________
IntroducingGraphing
Linear Equations
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Graphing Patterns
1) Study and complete the pattern.
2) Complete the table.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
0 1 2 3 4 5
step number of squares
0
1
2
3
4
5
What is the slope? ___________ Show the slope on the pattern, table and graph.
What is the y-intercept? _______ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: _____________________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
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Graphing Patterns
1) Study and complete the pattern.
2) Complete the table.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
0 1 2 3 4 5
step number of squares
0
1
2
3
4
5
What is the slope? ___________ Show the slope on the pattern, table and graph.
What is the y-intercept? _______ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: _____________________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
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Graphing Patterns
1) Study and complete the pattern.
2) Complete the table.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
0 1 2 3 4 5
step number of squares
0
1
2
3
4
5
What is the slope? ___________ Show the slope on the pattern, table and graph.
What is the y-intercept? _______ Show the y-intercept on the pattern, table and graph.
Use the slope and y-intercept to write the equation: _____________________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
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Graphing Patterns
1) Study and complete the pattern.
2) Complete the table.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
0 1 2 3 4 5
step number of squares
0
1
2
3
4
5
Can you determine a slope? _______Why or why not?______________________
What is the y-intercept? _______ Show the y-intercept on the table, graph and rule.
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 4
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Graphing Number Patterns
1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 2, 5, 8, 11, ___, ___, ___, ___, ____,
x y
What is the slope? ___________ Show the slope on the table and graph.
What is the y-intercept? _______ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____________________
Use the equation to find the value of y when x = 10? _____________Use the equation to find the value of y when x = 100? _____________Use the equation to find the value of y when x = 1000? _____________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 5
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Graphing Number Patterns1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 9, 8, 7, 6, 5, ___, ___, ___, ____,
x y
What is the slope? __________ Show the slope on the table and graph.
What is the y-intercept? _______ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____________________
Use the equation to find the value of y when x = 10? _____________Use the equation to find the value of y when x = 100? _____________Use the equation to find the value of y when x = 1000? _____________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 6
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Graphing Number Patterns
1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 6, 6, 6, 6, 6, ___, ___, ___, ____,
x y
What is the slope? __________ Show the slope on the table and graph.
What is the y-intercept? _______ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____________________
Use the equation to find the value of y when x = 10? _____________Use the equation to find the value of y when x = 100? _____________Use the equation to find the value of y when x = 1000? _____________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 7
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Graphing Number Patterns
1) Study and complete the pattern.
2) Complete the table for x = 0, 1, 2, 3, 4, and 5.
3) Label the X and Y axes and graph the pattern.
4) Answer the questions.
X: 0 1 2 3 4 5 6 7 8
Y: 0, 1, 2, 3, 4, ___, ___, ___, ____,
x y
What is the slope? __________ Show the slope on the table and graph.
What is the y-intercept? _______ Show the y-intercept on the table and graph.
Use the slope and y-intercept to write the equation: _____________________
Use the equation to find the value of y when x = 10? _____________Use the equation to find the value of y when x = 100? _____________Use the equation to find the value of y when x = 1000? _____________
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
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Graphing Equations
1) Study the equation y = 3x + 1
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
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Graphing Equations
1) Study the equation y = 2x + 3
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 10
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Graphing Equations
1) Study the equation y = –2x + 8
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 11
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Graphing Equations
1) Study the equation y = –1x + 7
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 12
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Graphing Equations
1) Study the equation y = x
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
what is this type of equation called? ________
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 13
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Graphing Equations
1) Study the equation y = 3x + –6
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 14
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Graphing Equations
1) Study the equation y = 3
2) Looking at the equation, what is the slope? _____
what is the y-intercept? ______
3) Complete the table for x = 0, 1, 2, 3, 4 and 5.
4) Label the X and Y axes and graph the equation.
5) Answer the questions.
x y
Show the slope on the table and graph. Is this the same as your answer in #2? _____
Show the y-intercept on the table and graph. Is this the same as your answer in #2? __
Is the pattern linear or non-linear? __________________
Is the pattern ascending, descending, or horizontal? ____________
© Introducing Graphing Linear Equations - page 15
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Family of Lines
1) Study the equation y = 2x + 1 what is the slope? _____
what is the y-intercept? ______
2) Study the equation y = 2x + 3 what is the slope? _____
what is the y-intercept? ______
3) Study the equation y = 2x what is the slope? _____
what is the y-intercept? ______
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
x y x y x y
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What do you notice about the three lines? ______________________________
What do the equations of the lines have in common? ___________________________
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Family of Lines
1) Study the equation y = x + 2 what is the slope? _____
what is the y-intercept? ______
2) Study the equation y = x + 5 what is the slope? _____
what is the y-intercept? ______
3) Study the equation y = x + – 3 what is the slope? _____
what is the y-intercept? ______
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
x y x y x y
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What do you notice about the three lines? ______________________________
What do the equations of the lines have in common? ___________________________
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Family of Lines
1) Study the equation y = x + 2 what is the slope? _____
what is the y-intercept? ______
2) Study the equation y = 3x + 2 what is the slope? _____
what is the y-intercept? ______
3) Study the equation y = –2x + 2 what is the slope? _____
what is the y-intercept? ______
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
x y x y x y
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What do you notice about the three lines? ______________________________
What do the equations of the lines have in common? ___________________________
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Family of Lines
1) Study the equation y = 5 what is the slope? _____
what is the y-intercept? ______
2) Study the equation y = 2 what is the slope? _____
what is the y-intercept? ______
3) Study the equation y = –3 what is the slope? _____
what is the y-intercept? ______
4) Complete the table for each equation for x = 0, 1, 2, 3, 4 , 5.
5) Graph the three equations on the same graph.
x y x y x y
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What do you notice about the three lines? ______________________________
What do the equations of the lines have in common? ___________________________
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (3, 2).
2) Use the ruler to draw a line through the point (3, 2) with a slope of 2.
x y
3) Looking at the graph, what is the y-intercept? ______
what is the equation of the line? ___________
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? __________________
6) Is the pattern ascending, descending, or horizontal? ____________.
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (2,1).
2) Use the ruler to draw a line through the point (2,1) with a slope of –2.
x y
3) Looking at the graph, what is the y-intercept? ______
what is the equation of the line? ___________
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? __________________
6) Is the pattern ascending, descending, or horizontal? ____________.
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (3, 5).
2) Use the ruler to draw a line through the point (3, 5) with a slope of 0.
x y
3) Looking at the graph, what is the y-intercept? ______
what is the equation of the line? ___________
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? __________________
6) Is the pattern ascending, descending, or horizontal? ____________.
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Graphing a Line given
a Coordinate and the Slope
1) Label the graph and plot (1, 3).
2) Use the ruler to draw a line through the point (1, 3) with a slope of –1.
x y
3) Looking at the graph, what is the y-intercept? ______
what is the equation of the line? ___________
4) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
5) Is the pattern linear or non-linear? __________________
6) Is the pattern ascending, descending, or horizontal? ____________.
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Finding the Equation of a Line
x y
1) Study the graph.
2) Looking at the graph, what is the slope? _____
what is the y-intercept? ______
what is the equation of the line? ___________
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? __________________
5) Is the pattern ascending, descending, or horizontal? ____________.
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Finding the Equation of a Line
x y
1) Study the graph.
2) Looking at the graph, what is the slope? _____
what is the y-intercept? ______
what is the equation of the line? ___________
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? __________________
5) Is the pattern ascending, descending, or horizontal? ____________.
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Finding the Equation of a Line
x y
1) Study the graph.
2) Looking at the graph, what is the slope? _____
what is the y-intercept? ______
what is the equation of the line? ___________
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? __________________
5) Is the pattern ascending, descending, or horizontal? ____________.
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Finding the Equation of a Line
x y
1) Study the graph.
2) Looking at the graph, what is the slope? _____
what is the y-intercept? ______
what is the equation of the line? ___________
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? __________________
5) Is the pattern ascending, descending, or horizontal? ____________.
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Finding the Equation of a Line
x y
1) Study the graph.
2) Looking at the graph, what is the slope? _____
what is the y-intercept? ______
what is the equation of the line? ___________
3) Complete the table for x = 0, 1, 2, 3, 4 , and 5.
4) Is the pattern linear or non-linear? __________________
5) Is the pattern ascending, descending, or horizontal? ____________.
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Word Problem
Sabrina wants to buy a CD player. She has $2. She decides to save $3 from her allowance every week.
1) Complete a table and graph Sabrina’s savings during 10 weeks.
Number of weeks
(X)
Sabrina’s savings
(Y)
2) What is the slope?
3) What part of the word problem gives you the “slope”?
4) What is the y-intercept?
5) What part of the word problem gives you the “y-intercept”?
6) What is the equation that represents Sabrina’s savings?
7) What does the X-axis represent?
8) What does the Y-axis represent?
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Word Problem
Sabrina has $12 saved. She decides to spend $2 a week on candy.
1) Complete a table and graph Sabrina’s savings during 10 weeks.
Number of weeks
(X)
Sabrina’s savings
(Y)
2) What is the slope?
3) What part of the word problem gives you the “slope”?
4) What is the y-intercept?
5) What part of the word problem gives you the “y-intercept”?
6) What is the equation that represents Sabrina’s savings?
7) During what week did Sabrina run out of money? Label it on the graph.
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Word Problem
Sabrina wants to buy a CD player. She has no money. She decides to save $2 from her allowance every week.
1) Complete a table and on graph paper graph Sabrina’s savings during 10 weeks.
Number of weeks
(X)
Sabrina’s savings
(Y)
2) What is the slope?
3) What part of the word problem gives you the “slope”?
4) What is the y-intercept?
5) What part of the word problem gives you the “y-intercept”?
6) What is the equation that represents Sabrina’s savings?
7) What does the X-axis represent?
8) What does the Y-axis represent?
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Graphing Linear Systems of Equations
A) Sabrina has $30 and she receives an allowance of $5 per week.
B) Sergio has $10 and he receives an allowance of $10 per week.
1) Complete a t-table and graph Sabrina and Sergio’s savings for 10 weeks.
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? ____
What is the y-intercept? ____
What is the slope? ____
What is the y-intercept? ____
2) Graph Sabrina and Sergio’s savings for 10 weeks.
3) What part of problem gives you the “slope”?
4) What part of the word problem gives you the “y-intercept”?
5) What is the equation that represents Sabrina’s savings?
6) What is the equation that represents Sergio’s savings?
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During what week will Sabrina and Sergio’s savings be the same? _________
Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
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Graphing Linear Systems of Equations
A) Sabrina has $ 15 and she receives an allowance of $ 5 per week.
B) Sergio has $ 30 and he receives an allowance of $ 2 per week.
1) Complete a t-table and graph Sabrina and Sergio’s savings for 10 weeks.
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? ____
What is the y-intercept? ____
What is the slope? ____
What is the y-intercept? ____
2) Graph Sabrina and Sergio’s savings for 10 weeks.
3) What part of problem gives you the “slope”?
4) What part of the word problem gives you the “y-intercept”?
5) What is the equation that represents Sabrina’s savings?
6) What is the equation that represents Sergio’s savings?
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During what week will Sabrina and Sergio’s savings be the same? _________
Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
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Graphing Linear Systems of Equations
A) Sabrina has saved $ 70 and spends $ 5 per week.
B) Sergio has saved $ 60 and spends $ 3 per week.
1) Complete a t-table and graph Sabrina and Sergio’s spending until they run out of money.
Number of weeks
(X)
Sabrina’s savings
(Y)
Number of weeks
(X)
Sergio’ssavings
(Y)
What is the slope? ____
What is the y-intercept? ____
What is the slope? ____
What is the y-intercept? ____
2) Graph Sabrina and Sergio’s spending.
3) What part of problem gives you the “slope”?
4) What part of the word problem gives you the “y-intercept”?
5) What is the equation that represents Sabrina’s savings?
6) What is the equation that represents Sergio’s savings?
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During what week will Sabrina and Sergio’s have the same amount of money?
_________ Show your answer on the t-table and the graph.
During what weeks does Sabrina have more money than Sergio? Show your
answer on the t-table and the graph.
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Unit Summary
Using words, graphs, diagrams and examples, clearly explain each one
of the following mathematical terms:
❒ pattern
❒ slope
❒ y-intercept
❒ equation
❒ linear
❒ non-linear
❒ ascending
❒ descending
❒ horizontal
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Unit Summary Continue
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