Today:
Review for Thursday's Test This Week's Khan Academy Topics New Concept: The Slope of a Line
CW 3.5 Questions Answered (Due Tomorrow)
Progress Reports Thursday
February 16, 2016
But first...the final results from the thrilling world of Cricket...
1st Coordinate Plane Test: Thursday, Feb. 18; The Test will include the following:
Functions, Domain, Range Ordered Pair Solutions
Standard Form of a Line/Intercepts Slope of a Line
Grade
Trackers
For today, you need: Grade trackers, Notebook, graph paper,
calculatorWork the problems out. A wrong answer is far better than no answer..
Find Intercepts from a Linear Equation
2/21/16
Topic DueDate
Domain & Range from Graph 2/21/16
Interpreting Graphs of Linear & Non-Linear
Functions
2/21/16
WARM●UP Graph Paper
Out
●
●
Domain & Range from Graph
-3
9-3
6
Is the graph a function?Is the graph a
linear function?
Domain & Range from Graph
-6
6 -8
9
Is the graph a function?
Is the graph a linear function?
Domain & Range from Graph
Is the graph a function?
Is the graph a linear function?
-2
7
0 4
1. The x values in a relation are called the:
2. The range of this relation { (-2,1); (-4,1); (2,5); (-2,3); (4,8); } is: a) {-2,1,2,-2,4} b) {1,3,5,3,8} c) {1,1,5,3,8} d) {-2,1,2,-4,8} e) none3. Given y = -2x – 3, the f (-5) is: 4. What are the x and y intercepts for: 2x – 6 = y
5. Which ordered pair is not a solution to: y = 4x - 10
a) -13 b) 0 c) -3 d) 7 e) none
a) (0,4) b) (3,0) c) (3,-6) d) (-3,6) e) none
5 Question Test Review:
a) (1,-6) b) (0,-10) c) (-1,-6) d) (2,-2) e) none
Number your paper 1-5; do not say the answer out loud...
a) domain b) range c) ordered pair d) output e) none
Graph the equation with at least 3 points: 3y = 2x - 6
Can you simplify an equation, say, 4x - 6y =
12 and still get the same line?
Where/How to Start?- 2x +3y = -6; 2x - 3y = 62x - 3(0) = 6
x = 3
●
2(0) - 3y = 6
y = -2
●
●
Use the slope of the line to find one more point.
What is the y coordinate when x is 150?y =
98
...Find the intercepts
+
+
--
Graph paper out, try to work the problem completely!
y is 4 more than the product of 7 and x; x = 3
Write a function rule that represents each sentence. Then find the value of y for the given value of x.
You got the answer correct. That's good, but what does it mean?What do those two numbers represent?
y is 11 less than of x; x = 72
Write the following function rule in function notation. Again, find the value of
the function at the given x.f(x) = (72) - 11
f(x) = 13
y = 7(3) + 4; y = 25
Warm-Up
Find any other point on this same line.
2. Find the range values of the function for the given domain.
f(x) = -3x + 2 ; {-5, -2, 6}Steps1. Sub in each domain value one @
a time.2. Solve for y in each equation3. List y values in braces.The range values of the function f(x) = -2x + 3,
with a domain of {-5, -2, 6} are..... {17, 8, -16}
Test Review
What are three of the coordinates of this line? (-5, 17), (-2, 8),
(6, -16)
Test Review
Test Review
From the graph below, which equation contains point B?
Test Review
Class Notes Section of Notebook
The Slope of a Li
ne
x
y
x2 – x1
y2 – y1
change
in ychange in x
The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula
(x1, y1)
(x2, y2)
y2 – y1
x2 – x1
m = , (x1 ≠ x2 ).
The rise is the difference of the y-values of two points on a line.The run is the difference in the x-values of two points on a line.
The constant rate of change of a straight line is called the slope.
The Slope of a Line:
Slope is usually represented by the letter m (from the French, monter, which
means “to go up”).
Straight Lines (linear functions) are straight because the slope never changes!!
(3, 2)
(–1, –2)
Then count horizontally to a second point to find the run.
Count vertically from any one point on the line to find the rise.
Finding the Slope of a Line
slope = = 1
The slope of the line is 1.
It does not matter which ordered pair you start with.
slope = = 1
44
(5, 4)
Then count horizontally to a second point to find the run.
Count vertically from any one point on the line to find
the rise.
slope = =
The slope of the line is
slope = =
Find the slope of the line:
It does not matter which y you begin from.
(1, 2)
The Slope of a Line
The slope of a line is the ratio of rise to run for any two points on the line.change in y
change in x Rise Run=
Find the slope of the line passing through the points (2, 3) & (4, 5).
The x1 and y1 must come from the same ordered pair.
y2 – y1
x2 – x1
m = 5 – 3 4 – 2
= = 22
= 1
2
2(2, 3)
(4, 5)
x
y
The Slope of a Line
Name one other ordered pair on this
line.
The Slope of a LineWhat is the slope of this, and all horizontal lines?Don't guess,
just plug the numbers in...
All horizontal lines have a slope of zero.
The Slope of a LineWhat is the slope of this, and all vertical lines?
All vertical lines have a slope that is undefined because... a
denominator cannot be zero.
y
x2-2
The slope of a line is a number, m, which measures its steepness.
m = 0
m = 2
m is undefined
m =12
m = - 14
The slope of a line reveals how the f(x) is affected by a change in x
What does a steeper line tell you about the y
variable?
y2 – y1
x2 – x1m =
The Slope of a Line
The Slope of a Line
What is the slope of the line?
The Slope of a Line
What is the equation of this line?
The point here,
is called the....y-intercept. We know the
slope, and the y-intercept, so...
y = x - 2
What is the slope of this line?
The Slope of a Line
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