Exercise
Solve 2y + 4 = 10.
y=3
Exercise
Solve y − x = 5.
y=x+5
Exercise
Solve x + y = 5.
y = −x + 5
Exercise
Solve −6x + y = 12.
y = 6x + 12
Exercise
Solve −6x + 2y = 12.
y = 3x + 6
Y-intercept
The y-intercept is the point
where a line crosses the
y-axis.
X-intercept
The x-intercept is the point
where a line crosses the
x-axis.
Example 1
Find the x- and y-intercepts
of the line 2x + 3y = 6 and use
them to graph the line.
2(0) + 3y = 6 2x + 3(0) = 6
3y = 6
2x = 6
2 2
3 3
y=2
x=3
y
x
Slope-intercept form
The slope-intercept form of
a linear equation is
y = mx + b.
The slope of the line is m,
and the y-intercept is at
(0, b).
Example 2
Find the slope and y-intercept
of y = 3x − 2.
The equation is in slopeintercept form, y = mx + b.
The slope is m = 3.
Since b = −2, the y-intercept
is (0, −2).
Example 3
Change 2x − y = 10 to slopeintercept form.
2x − y = 10
− 2x
− 2x
−y = −2x + 10
−1 −1
−1
y = 2x − 10
Graphing an Equation
Using the
Slope-Intercept Form
1. Solve the equation for y
to put it in slopeintercept form.
2. Plot the y-intercept at
(0, b).
Graphing an Equation
Using the
Slope-Intercept Form
3. Express the slope (m) as
a ratio to find the rise and
run.
Graphing an Equation
Using the
Slope-Intercept Form
4. From the y-intercept, use
the rise and run to graph
two other points.
5. Draw a line through the
points.
y
x
Example 4
Use the slope-intercept form
to graph the line y = 3x − 2.
1. Identify the y-intercept as
(0, −2) and plot it on the
graph.
2. Express the slope as a ratio
to find rise and run:
3
rise
m = 3 = 1 = run .
Example 4
Use the slope-intercept form
to graph the line y = 3x − 2.
3. From (0, −2),move up three
and right one to plot a
second point on the line,
(1, 1).
4. Draw a line through the
two points.
Example 4
Use the slope-intercept form
to graph the line y = 3x − 2.
3
rise
5. Use m = 3 = 1 = run
to check your graph. From
(0, −2) move down three
and left one to plot a third
point.
y
x
Example 5
Graph the line 2x + 3y = 3.
2x + 3y = 3
− 2x
− 2x
3y = −2x + 3
3
3
3
−2x
y= 3 +1
y
x
Example
Find the x- and y-intercepts
of the line 3x + 2y = 12.
(4, 0) and (0, 6)
Example
What are the
x- and y-intercepts of y = 5?
Note that y = 5 no matter what
x is, so the y-intercept is
(0, 5). If y = 0, then the
equation becomes 0 = 5,
which is not true.
There is no x-intercept.
Example
What are the
x- and y-intercepts of x = 5?
Note that x = 5 no matter what
y is, so the x-intercept is
(5, 0). If x = 0, then the
equation becomes 0 = 5,
which is not true.
There is no y-intercept.
Example
Determine the slope and
y-intercept of 6x + 4y = 3 by
converting to slope-intercept
form.
3
3
y=− x+
2
4
3
3
(0, )
m=−
2
4
Example
Graph the line y = −3x.
y
x
Example
Graph the line y = 3x − 2.
y
x
Exercise
Write an equation for a line
with the these characteristics:
slope of 4 and y-intercept
(0, 12).
y = 4x + 12
Exercise
Write an equation for a line
with the these characteristics:
slope of 0 and y-intercept
(0, −9).
y = −9
Exercise
Write an equation for a line
with the these characteristics:
undefined slope and
x-intercept (5, 0).
x=5
Exercise
Write an equation for a line
with the these characteristics:
x-intercept (3, 0) and
y-intercept (0, 6).
y = −2x + 6