4.7 Graphing Using Slope-

Intercept Form

Hopefully you remember from last section, that we can graph a line easily when given:

1. a random point2. the slope of the line

Let’s do an example of this:

Point (2,3)

Slope = 2

Wouldn’t it be great if we could just look at an equation and figure out it’s slope and a point???!!!

WE CAN!!! YAHHHH!!!!

BY USING SLOPE-INTERCEPT FORM

SLOPE-INTERCEPT FORM

EXAMPLE #1

So all we have to do issolve for “y” and we can see a slope and a point!!!

Some more examples…

“b” is the y-intercept

€

y =43x − 4

So in order to use this form we must solve

for “y”

Let’s practice converting an equation to slope-intercept

form.In other words: SOLVE FOR “y”1. 2x – y = -3 2. 4x + 2y = 6

3. -5x – 3y = 15 4. 4x + 3y = 24

-2x -2x -y = -2x – 3 y = 2x + 3

-4x -4x 2y = -4x + 6 y = -2x + 3

+5x +5x -3y = 5x + 15

€

y =−53x −5

-4x -4x 3y = -4x + 24

€

y =−43x +8

Now let’s look at each equation and decide what the slope and y-intercept is.

1. y = -3x + 6 2. y = 2x – 5

3. y = -x 4. 2y = 8x +10

5. x + 3y = 9 6. x – 2y = 16

m = b = (0,6)

€

−31

m = b = (0,-5)

m = b = (0,0) m = b = (0,5)

m = b = (0,3) m = b = (0,-8)

€

21

€

−11

€

41

€

−13

€

12

y = 4x + 5

€

y =−13x + 3

€

y =12x −8

y = mx + b

EVERYBODY GET A COMMUNICATOR!!

Now we can finally graph using slope-

intercept form.y = -3x + 2

m =

b = (0,2)€

−31

y = mx + b

Graph using slope-intercept form.

x + y = 0

m =

b = (0,0)€

−11

y = -x

y = mx + b

Graph using slope-intercept form.3x - 3y = 9

m =

b = (0,-3)€

11

y = x - 3

-3x -3x-3y = -3x + 9-3 -3 -3

Graph using slope-intercept form.4x + 5y = 15

m =

b = (0,3)€

−45€

y =−45x + 3

-4x -4x5y = -4x + 155 5 5

Graph using slope-intercept form.4x - y – 3 = 0

m = b = (0,-3)

€

41

€

y = 4x − 3

-4x -4x- y – 3 = -4x +3 +3-y = -4x + 3

Graph using slope-intercept form.2x - 3y – 6 = 0

m =

b = (0,-2)€

23

€

y =23x −2

-2x -2x-3y – 6 = -2x +6 +6-3y = -2x + 6-3 -3 -3

Graph using slope-intercept form.x – y + 4 = 0

m =

b = (0,4)€

11

€

y = x + 4

-y + 4 = -x -4 -4-y = -x - 4

-1 -1 -1

-x -x

Graph using slope-intercept form.

m =

b = (0,1)€

12

€

y =12x +1

Now I want you to graph these two equations on the same

graph

m =

b = (0,3)€

31

€

y = 3x + 3

€

y = 3x −2

m =

b = (0,-2)€

31

THESE LINES ARE PARALLEL!!

THEY HAVE THE SAME SLOPE

y = mx + b

Are these lines parallel???a.) -x + 2y = 6 b.) -x + 2y = -2

c.) x + 2y = 4

+x +x2y = x + 62 2 2

€

y =12x + 3

+x +x2y = x - 22 2 2

€

y =12x −2

-x -x2y = -x + 42 2 2

€

y =−12x +2

“a” and “b” are parallel

y = mx + b

For each problem, tell me if the two equations are parallel. y = mx + b

1. y = -3x + 2 y + 3x = -42. 2x – 12 = y y = 10 + 2x3. y = x + 8 x – y = -14. 2x – 5y = -3 5x + 2y = 6

y = -3x - 4Yes!!!!!y = 2x - 12y = 2x + 10Yes!!!!!

y = x + 1 Yes!!!!!

€

y =25x +35

€

y =−52x + 3

No!!!!

Write the equation of a line that has a y-intercept of -3

and a slope of -4.1.y = -3x – 42.y = -4x – 33.y = -3x + 44.y = -4x + 3

Write an equation of the line that goes through the points

(0, 1) and (1, 4).1.y = 3x + 42.y = 3x + 13.y = -3x + 44.y = -3x + 1

-3 -3 -3

Find the slope and y-intercept.4) 5x - 3y = 6

Write it in slope-intercept form. (y = mx + b)

5x – 3y = 6 -3y = -5x + 6

y = x - 253

m =

b = -2

53

Write it in slope-intercept form. (y = mx + b)

2y + 2 = 4x 2y = 4x - 2

y = 2x - 1

Find the slope and y-intercept.

5) 2y + 2 = 4x

2 2 2 m = 2b = -1

Find the slope and y-intercept of y = -2x + 4

1.m = 2; b = 4

2.m = 4; b = 2

3.m = -2; b = 4

4.m = 4; b = -2