2.3 graphing linear equations in slope-intercept form

2.3 Graphing Linear Equations in Slope-Intercept Form

Intercepts

X-intercept

• Graph crosses the x axis

• It occurs when y=0

• (x- intercept, 0)

Y-intercept

• Graph crosses the y-axis

• It occurs when x=0

• (0, y-intercept)

4

3

2

1

-1

-2

-3

-6 -4 -2 2 4 6

A

B

y - intercept

x - intercept

y

X

Slope-Intercept Formy = mx + b

slopeslope y-intercepty-intercept

Find the slope and y-intercept ofy = -5x + 6

5m 6b

If the equation is not in y=mx +b form….

Solve for y

Find the slope and y-intercept of2y = 7x - 4

7

2m 2b

2 2 2

72

2y x

Find the slope and y-intercept of2x + 3y = 6-2x -2x

3y = - 2x + 63 3 3

23

2 xy

2

3m 2b

Find the slope and y-intercept of-7x - 5y = 25+7x +7x

-5y = 7x + 25-5 -5 -5

55

7 xy

7

5m 5b

Steps To Graph Using y=mx+bSlope Intercept From:

• 1.) Solve for y so your equation is y=mx+b• 2.) Plot your b (y-intercept) on the y-axis• 3.) From your y intercept use your slope to

go up(+) or down (-) and right and plot your 2nd point

• 4.) Now that you have 2 points draw your line

5

4

3

2

1

-1

-2

-3

-4

-8 -6 -4 -2 2 4 6

Using y-intercept and slope, graph:

52

3y x

5

4

3

2

1

-1

-2

-3

-4

-8 -6 -4 -2 2 4 6

Using y-intercept and slope, graph:

24

5y x

Using y-intercept and slope, graph:

3 7y x

How to Identify the x-intercept

Algebraically

• Set y=0 and solve for x

Geometrically

• Look at where the graph crosses the x axis (can only be done if graph is precise)

Identify the x-intercept: y-10 = -5x

Algebraically Geometrically

10 5y x 0 10 5x

10 5x 5 52 x(2,0)

5 10y x 5

, 101

m b

Assignment

TB: Page 62 (1,2,4-24 even, 29-33 all)