Ch 4.7

Objective:

To use the slope and y-intercept to

graph lines.

Definitions

Slope-Intercept Form

Slope (m) and y-intercept (b) written in the form: y = mx + b

Parallel Lines

Parallel lines have the SAME SLOPE but different y-intercepts

 

Rules

Steps for Graphing

1) Plot the y-intercept point: (0, b)

2) Plot a second point using m = rise/run

3) Draw a line through the two points

Slope-Intercept Form of the Linear Equation

Any linear equation which is solved for y is inslope-intercept form.

y = mx + b

Find the slope and y-intercept of the following linear equations:

1) y = 3x + 4

2) y = -2x - 1

3) y = 5x

4) y = x - 458

5) y = x --29

14

6) y = 6

m = 3 b = 4

m = -2 b = -1

m = 5 b = 0

m = b = -458

m = b =-29

-14

m = 0 b = 6

Parallel Lines: Example 1

 Are these lines parallel?

y = 3x + 2 y = 3x + 5

These equations both have slope (m=3)

but they have different y-intercepts [(0, 2) & (0, 5)]

Tell whether the lines below are parallel.

1) 3x + y = 7 y = -3x + 1-3x -3x

y = -3x + 7

m = -3

y = mx + b

m = -3

Lines are parallel!

Same slope!

Example #1Graph: y = 2x + 3

1) Plot the point (0,3)

2) m = 2 (2 units up and 1 unit over) so a second point would be (1,5)

1

3) Draw a line through the two points

Graph the line which passes through (-2, 1) and has a slope of -3.

x

y

1) Plot the point.Steps

2) Write slope as fractionand count up and over.

m = -3 = -31 -3

+1or m =

3-1

3) Draw line through points.

Example 2

Graph the line which passes through (3, 2) and has a

slope of .

x

y

1) Plot the point.Steps

2) Write slope as fractionand count up and over.

m =34

+3

+4

or m = -3-4

3) Draw line through points.

34

Example 3

Graph the line which passes through (-5, 4) and has a

slope of .

x

y

1) Plot the point.Steps

2) Write slope as fractionand count up and over.

m = -32

-3

+2

3) Draw line through points.

-32

Example 4

-3

Graph the following linear equation using slope and y-intercept.

x

y

1) Find the slope and y-intercept.Steps

2) Plot the y-intercept.

m =23 or m =

-2

4) Draw line through points.

y x= −23

1

m =23

b =−1

3) Plot the slope.

+2+3

-2

-3

Example 5

-1

-2

Graph the following linear equation using slope and y-intercept.

x

y

1) Find the slope and y-intercept.Steps

2) Plot the y-intercept.

m = -12 or m =

1

4) Draw line through points.

y x=− +12

4

m =−12

b =4

3) Plot the slope.

+2

+1-2

Example 6

Slope-Intercept Form of the Linear Equation

Write a linear equation in the form y = mx + bgiven the following.

1) m = 2, b = -3

2) m = , b = 5

3) m = , y-int.= 2

2

3

−3

7

4) m = 0, b = 6

5) m = , b = 0

6) m = 1, b =

−1

2

−2

3

y = 2x - 3

y x= +23

5

y x=− +37

2

y = 6

y x=−12

y x= −23

Write a linear equation in slope-intercept formto describe each graph.

x

y

x

y

b = 3 m =21

y = 2x + 3

b = -4 m =−13

y x=− −13

4

Parallel Lines

Graph the following on the coordinate plane.

y x= −12

3 y x= −12

1

m =12

b =−3

m =12

b =−1x

y

Parallel lines have the same slope.

Write a linear equation to describe this situation and graph.

Kyle has $300 and is saving $25 a week.

Let x = # of weeks Let y = savings in dollars

y = 25x + 300

change start value

y = mx + bSlope Y-intercept

Sav

ings

Weeks

500

400

300

200

100

00 1 2 3 4 5

m = $25 / week

b = 300

Pam received $100 and spends $4 each week.

1) Write an equation for the money, y, she has after x weeks.

2) What are the slope and y-intercept?

y = 100 - 4x

m = -4

b = 100