1. Objective
graph linear equations using slope-intercept form

2. Slope Review The slope m of a line passing through two points
and is the ratio of the rise change to the run. y
run
rise x

3. Section 4.5 “Graph Using Slope-Intercept Form”
a linear equation written in the form
y-coordinate
x-coordinate
y = mx + b
slope
y-intercept

4. Identifying Slope and the Y-Intercept
Slope of 3 means:
y = 3x + 4
y = mx + b
The equation is in the form y
= m x + b.
So, the slope
of the line is 3, and the y-intercept is 4.
3x + y = 2
Rewrite the equation in slope-intercept form by solving for y.
y = 2 – 3x
Is this in slope-intercept form?
The line has a slope of – 3 and a y-intercept of 2.
y = -3x + 2

5. Identify the slope and y-intercept of the line with the given equation.
3x – 3y = 12
Rewrite the equation in slope-intercept form by solving for y.
3x – 12
= 3y
Rewrite original equation. y
3x – 12 = 3
Divide 3 by equation. y
x – 4 =
Simplify.
ANSWER
The line has a slope of 1 and a y-intercept of –4.

6. Graph the equation y = 2 - 2x.
Graph an Equation Using the Slope-Intercept Form
Graph the equation y = 2 - 2x.
y-axis 5 4
Rewrite in slope-intercept form 3 2 1
slope
y-intercept -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
x-axis
Slope of
-2 means: -1 -2 OR -3
Slope of
-2 means: -4 -5

7. Graph the equation y = -3 + 2/3x.
Graph an Equation Using the Slope-Intercept Form
Graph the equation y = /3x.
y-axis 5 4
Rewrite in slope-intercept form 3 2 1
slope
y-intercept -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
x-axis
Slope of
2/3 means: -1 -2 OR -3
Slope of
2/3 means: -4 -5

8. Graph Using Slope and the Y-Intercept
Graph the equation 2x + y = 3.
STEP 1
Slope of -2 means:
Rewrite the equation in slope-intercept form. y
– 2x + 3 =
STEP 2
Identify the slope and the y-intercept.
= – 2 m
and
= 3 b
STEP 3
Plot the point that corresponds to the y-intercept,(0, 3).
STEP 4
Use the slope to locate a second point on the line. Draw a line through the two points.

9. Graph Using Slope and the Y-Intercept
Graph the equation 3y – 2x = 3.
Slope of 2/3 means:
STEP 1
Rewrite the equation in slope-intercept form.
y = 2 3 x
STEP 2
Identify the slope and the y-intercept.
= 2/3 m
and
= 1 b
STEP 3
Plot the point that corresponds to the y-intercept,(0, 1).
STEP 4
Use the slope to locate a second point on the line. Draw a line through the two points.

10. Parallel Lines
two lines in the same plane are parallel if they never intersect. Because slope gives the rate at which a line rises or falls, two lines with the SAME SLOPE are PARALLEL.

11. Line a and line c have the same slope, so they are parallel.
Determine which of the lines are parallel.
Find the slope
of each line.
– 1 – 0
– 1 – 2 =
– 1
– 3 1 3 =
Line a: m =
– 3 – (–1 )
0 – 5
– 2
– 5 = 2 5 =
Line b: m =
– 5 – (–3)
– 2 – 4
– 2
– 6 = 1 3 =
Line c: m =
Line a and line c have the same slope, so they are parallel.