Complete the following problems in your lecture notebook, QUIETLY.1) Find the slope of the line given (2, 3) and (-3, -2).

2) Write the equation y – 5 = 6(x – 8) in slope-intercept form.

3) Write the equation y + 7 = -8(x + 5) in slope-intercept form.

Announcements:•Unit 1 Retake is tomorrow after school.•Unit 1 Test Corrections are due 9/19/12.

Do Now

Students will be able to demonstrate their understanding of graphing linear

equations by correctly graphing at least 3 of the 4 linear equations on their exit slip.

Objective

Ex. x – y = 6 y = x – 6

• Step 1: Plot your y-intercept on your graph.

• Step 2: Rewrite your slope as a fraction.

• Step 3: The numerator is the vertical change (RISE) & the denominator is the horizontal change (RUN).

• Step 4: Graph at least 2 points and connect the dots.

Rules for Graphing in Slope-intercept formy = mx + b

• Step 1: Rewrite your equation in slope-intercept form.

• Follow the steps for Graphing in slope-intercept form.

Rules for Graphing in Standard form.Ax + By = C

Example 1: Graph y = ½x – 7.

Step 1 The y-intercept is –7. So graph (0, –7).

From (0, –7), move up 1 unit and right 2 units. Draw a dot.

Step 3 Draw a line through the points.

Step 2 The slope is 1/2 .

Example 2: Graph 5x + 4y = 8.

Step 2 The y-intercept is 2, so graph (0, 2).

From (0, 2), move down 5 units and right 4 units. Draw a dot. Draw a line connecting the points.

Step 3 The slope is

Step 1 Write the equation in slope-intercept form

Example 3: Graph the line given the slope & y-intercept.

y intercept = 4

Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4).

Step 3 Draw the line through the two points.

•

••

•

Run = 5

Rise = –2

Step 2 Slope = Count

2 units down and 5 units right

from (0, 4) and plot another point.

y

slope = 4; y-intercept =

Step 1 The y-intercept is , so the

line contains (0, ). Plot (0, ).

Step 3 Draw the line through the two points.

•

•Rise = 4

Run = 1

Example 4: Graph the line given the slope and y-intercept.

Step 2 Slope = Count

4 units up and 1 unit right from

(0, ) and plot another point.

Example 5: Graph y = 3x – 1 slope: m = 3 =

y-intercept: b = –1

Step 1 Plot (0, –1).

Step 2 Count 3 units up and 1 unit right and plot another point.

Step 3 Draw the line connecting the two points.

•

•

Example 6: Graph 2y + 3x = 6

Step 1 Write the equation in slope-intercept form.

Step 2 Graph the line.

slope: m =

y-intercept: b = 3

Plot (0, 3). •

•

Step 3 Count 3 units down and 2 units right and plot another point. Draw the line connecting the two points.

YOU TRY! #1

Graph the line given the slope and y-intercept.

slope = 2, y-intercept = –3

Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3).

•

•

Step 3 Draw the line through the two points.

Rise = 2

Run = 1Step 2 Slope =

Count 2 units up and 1 unit right

from (0, –3) and plot another

point.

Graph each line given the slope and y-intercept.

slope = , y-intercept = 1

YOU TRY! #2

Step 1 The y-intercept is 1, so the line contains (0, 1). Plot (0, 1).

•

Step 3 Draw the line through the two points.

•

Rise = –2

Run = 3

Step 2 Slope = Count 2 units down and 3 units right from (0, 1) and plot another point.

YOU TRY! #3Graph the line described by the equation.

Step 1 Plot (0, 0).

Step 2 Count 2 units up and 3 units right and plot another point.

Step 3 Draw the line connecting the two points.

y = x + 0 is in slope-intercept form slope: m = 2/3 &

y-intercept: b = 0

•

•

YOU TRY! #4

6x + 2y = 10

Step 1 Write the equation in slope intercept form.

Write the equation in slope-intercept form. Then graph the line described by the equation.

Step 2 Graph the line.

y-intercept: b = 0

• Plot (0, 5).

slope: m =

• Count 3 units down and 1 unit right and plot another point.

• Draw the line connecting the two points.

•

•

y = –3x + 5

YOU TRY! #5

y = –4

Step 1 Plot (0, –4).

y = –4 is in the form y = mx + b.

y-intercept: b = –4

slope: m = 0 = = 0

Since the slope is 0, the line will be a horizontal at y = –4. •

Graph the line described by the equation.

Graph y = 2x – 4YOU TRY! #6

Graph 3x + 2y = 6.YOU TRY! #7

Write the equation in slope-intercept form and then graph the line. 6x + 2y = 10

y = –3x + 5

Reminder by the end of this lesson you will be expected to do this.