Graphing Using x and y Intercepts
Once we know both the xintercept and the yintercept, we can
graph the equation.
Example 1
Graph 3x + 5y = 15 using the x and y intercept.
Solution
First, find the intercepts.
To find the y intercept, let
x = 0. 
To find the xintercept, let
y = 0. 
3 Â· 0 + 5y 
= 15 
3x + 5 Â· 0 
= 15 
5y 
= 15 
3x 
= 15 
y 
= 3 
x 
= 5 
The yintercept is 3. 
The xintercept is 5. 
The ordered pair is (0, 3). 
The ordered pair is ( 5, 0) 
We now graph these two points and draw the line that contains
them.
SlopeIntercept Form
The slopeintercept form is a special case of the pointslope
form, where the given point of the line (x_{ 0} , y_{
0} ) lies on the yaxis, so x_{ 0} = 0. This means
that the equation is of the form y  y_{ 0} = mx, or y =
mx + y_{ 0} . So, the equation is given explicitly when
we know both the intercept and the slope and it is simpler than
the more general pointslope form. This is the most common form
for the equation of a line.
Key Idea An equation for a line is said to be
in slopeintercept form when it is of the form y = mx + b, where
m is the slope of the line and b is the ycoordinate of the
yintercept. Any line that is not vertical has an equation that
can be written in slopeintercept form.
The equation of a vertical line cannot be written in
slopeintercept form because the slope of a vertical line is
undefined; that is, it has no slope.
