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Lesson 2.4 Quick Graphs of Linear Equations. Keywords: y-intercept x-intercept Slope-intercept form Standard form of a linear equation. GOAL: Use slope-intercept form and standard form to graph equations. 3. –. y. x. 2. =. SOLUTION. 4.

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Presentation Transcript
slide1

Lesson 2.4

Quick Graphs of Linear Equations

slide2

Keywords:

y-intercept

x-intercept

Slope-intercept form

Standard form of a

linear equation

slide4

GOAL:

Use slope-intercept form and standard form to graph equations.

slide5

3

y

x

2.

=

SOLUTION

4

Write the equation in slope-intercept form by adding to each side:

STEP 1

3

x

4

3

(

).

0, 2

+

y

x

2.

=

4

Find the y-intercept. Comparing

to , you can see that b2. Plot a point at

STEP 2

3

+

y

x

2

=

4

+

y

mx

b

=

=

Example 1

Use Slope-Intercept Form to Graph a Line

Graph

slide7

STEP 3

3

m

=

4

(

)

0, 2

(

)

4, 5

STEP 4

Draw a line through the two

points.

3

rise

=

run

4

Example 1

Use Slope-Intercept Form to Graph a Line

Find the slope. The slope is

, so .

From , move up 3 units

and right 4 units. Plot a

Second point at .

slide8

Checkpoint

1.

ANSWER

1

y

x

=

2

Use Slope-Intercept Form to Graph a Line

Graph the equation.

slide9

Checkpoint

ANSWER

2

y

x

=

Use Slope-Intercept Form to Graph a Line

Graph the equation.

2.

slide10

Checkpoint

ANSWER

2

y

3

x

=

3

Use Slope-Intercept Form to Graph a Line

Graph the equation.

3.

slide12

Example 2

(

)

2

0

Graph .

3x

+

2y

12

SOLUTION

=

Method 1 Use Standard Form

3x

+

12

Let .

y

0

=

=

x

4

Solve for x.

=

Draw Quick Graphs

STEP 1 The equation is already written in standard form.

STEP 2 Find the x-intercept.

The x-intercept is 4, so plot the point (4, 0).

slide13

Example 2

(

)

3

0

+

2y

12

=

y

6

Solve for y.

=

Let .

STEP 4 Draw a line through the intercepts.

x

0

=

Draw Quick Graphs

STEP 3 Find the y-intercept.

The y-intercept is 6, so plot the point (0, 6).

slide14

Example 2

+

2y

12

3x

=

2y

+

12

Solve for y.

3x

=

Standard form

3

x

2

y

+

6

Slope-intercept form

=

Now graph using the method of

Example 1.

Draw Quick Graphs

Method 2 Use Slope-Intercept Form

Solve for y to rewrite the equation

slide15

Checkpoint

ANSWER

y

+

3

=

4.

x

+

y

7

=

1

x

2

ANSWER

5.

Draw Quick Graphs

Graph the equation. Choose either method.

slide16

Checkpoint

5x

+

2y

10

ANSWER

=

6.

Draw Quick Graphs

Graph the equation. Choose either method.

slide18

Example 3

y

+

4

=

3x

y

+

4.

=

3x

c.

Graph the line that is perpendicular to the graph of

at its y-intercept.

y

+

4

=

3x

SOLUTION

a.

Draw the graph of using

the y-intercept 4 and slope 3.

y

+

4

=

3x

(

0, 1

)

Graph Parallel and Perpendicular Lines

a.

.

Draw the graph of

b.

Graph the line that passes through and is parallel to the graph of

slide19

Example 3

y

+

4

=

3x

(

)

0, 4

(

)

3, 3

The slope of any line perpendicular

to the graph of is the

negative reciprocal of 3, or . So,

from move down 1 unit and

right 3 units. Plot a second point

at . Draw the line.

c.

(

).

0, 1

1

(

),

y

0,1

+

4

=

3x

3

(

)

1, 2

Graph Parallel and Perpendicular Lines

b.

Graph the point Any line

parallel to the graph of

has the same slope, 3. From

move up 3 units and right 1 unit.

Plot a second point at . Draw

a line through the two points.

slide20

Checkpoint

y

2x

1

=

ANSWER

Graph Parallel and Perpendicular Lines

Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept.

7.

slide21

Checkpoint

ANSWER

Graph Parallel and Perpendicular Lines

Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept.

3

y

x

+

2

8.

=

4

slide22

Checkpoint

1

x

+

1

y

9.

=

5

ANSWER

Graph Parallel and Perpendicular Lines

Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept.