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 point
2. 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 is
solve for “y” and we
can see a slope and a point!!!
Some more examples…
4
y  x4
3

“b” is the y-intercept
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
-2x
-2x
-y = -2x – 3
y = 2x + 3
-4x
-4x
2y = -4x + 6
y = -2x + 3
3. -5x – 3y = 15
+5x
+5x
-3y = 5x + 15
4. 4x + 3y = 24
5
y
x 5
3
-4x
-4x
3y = -4x + 24
4
y
x 8
3
Now let’s look at each equation and decide
what the slope and y-intercept is. y = mx + b
1. y = -3x + 6
m=
3
1
2. y = 2x – 5
b = (0,6)
m=
3. y = -x

m=
1
1
b = (0,0)

m=
1
3
b = (0,3)
b = (0,-5)
4. 2y = 8x +10

5. x + 3y = 9
1
y
x3
3
2
1
m=
4
1
y = 4x + 5
b = (0,5)
6. x – 2y = 16

m=
1
2
1
y  x 8
2
b = (0,-8)
EVERYBODY GET A
COMMUNICATOR!!
Now we can finally graph
using slope-intercept form.
y = -3x + 2
m=
3
1
b = (0,2)

y = mx + b
Graph using slope-intercept
y = mx + b
form.
x+y=0
y = -x
m=
1
1
b = (0,0)

Graph using slope-intercept
3x - 3y = 9
form.
-3x
-3x
-3y = -3x + 9
-3
-3 -3
y=x-3
m=
1
1
b = (0,-3)

Graph using slope-intercept
4x + 5y = 15
form.
-4x
-4x
5y = -4x + 15
5
5
5
4
y
x3
5
m=
4
5
b = (0,3)
Graph using slope-intercept
4x - y – 3 = 0
form.
-4x
-4x
- y – 3 = -4x
+3 +3
-y = -4x + 3
y  4x  3
4
1
m=
b = (0,-3)
Graph using slope-intercept
2x - 3y – 6 = 0 form.
-2x
-2x
-3y – 6 = -2x
+6 +6
-3y = -2x + 6
-3
-3 -3
y
2
x 2
3
m=
2
3
b = (0,-2)
Graph using slope-intercept
x–y+4 =0
form.
-x
-x
-y + 4 = -x
-4 -4
-y = -x - 4
-1 -1 -1
y  x4
m=
1
1
b = (0,4)
Graph using slope-intercept
form.
1
y  x 1
2
m=
1
2
b = (0,1)


Now I want you to graph these two
equations on the same graph
y  3x  3
m=
3
1
b = (0,3)
y  3x  2
3
m=
1
b = (0,-2)
THESE LINES ARE
PARALLEL!!
THEY HAVE THE
SAME SLOPE
y = mx + b
Are these lines parallel???
a.) -x + 2y = 6
b.) -x + 2y = -2
+x
+x
+x
+x
2y = x + 6 y = mx + b 2y = x - 2
2
2 2
2
2
2
1
y
2
x3
1
y  x 2
2
c.) x + 2y = 4

-x
-x
2y = -x + 4
2
2 2

y
1
x 2
2
“a” and “b” are

parallel
For each problem, tell me if the two
equations are parallel.
y = mx + b
1. y = -3x + 2
y = -3x - 4 Yes!!!!!
y + 3x = -4
2. 2x – 12 = y
y = 2x - 12
Yes!!!!!
y = 10 + 2x
y = 2x + 10
3. y = x + 8
Yes!!!!!
x – y = -1
y=x+1
2
3
4. 2x – 5y = -3
y  x
5
5
No!!!!
5
5x + 2y = 6
y
x3

2
Write the equation of a line that has a yintercept of -3 and a slope of -4.
1. y = -3x – 4
2. y = -4x – 3
3. y = -3x + 4
4. y = -4x + 3
Write an equation of the line that goes
through the points (0, 1) and (1, 4).
1. y = 3x + 4
2. y = 3x + 1
3. y = -3x + 4
4. y = -3x + 1
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
-3
-3 -3
y=5 x-2
3
5
m=
3
b = -2
Find the slope and y-intercept.
5) 2y + 2 = 4x
Write it in slope-intercept form. (y = mx + b)
2y + 2 = 4x
2y = 4x - 2
2 2
2
y = 2x - 1
m=2
b = -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