Intercepts of a Line
Example
Given the equation 4x  3y = 12:
a. Find the xintercept.
b. Find the yintercept.
c. Use the intercepts to graph the line.
a. 
Solution
The xintercept has the form (a, 0).
To find the xintercept, substitute 0
for y.
Then solve for x.
Simplify.
Divide both sides by 4.
The xintercept is (3, 0). 
4x  3y
4x  3(0)
4x
x 
= 12
= 12
= 12
= 3 
b. 
The yintercept has the form (0, b).
To find the yintercept, substitute 0
for x.
Then solve for y.
Simplify.
Divide both sides by 3.
The yintercept is (0, 4). 
4x  3y
4(0)  3y
3y
y 
= 12
= 12
= 12
= 4

c. 
To graph the line 4x  3y = 12, plot the xintercept and the
yintercept.
Then, draw a line through the intercepts.
As a check, it is a good idea to find a third point on the line.
For example, choose 6 for x in the equation 4x  3y = 12.
Solve for y. The result y = 4.
Since (6, 4) is a solution of the equation 4x  3y = 12, the line should
pass through the point (6, 4). 
x 
y 

3 
0 
xintercept 
0 
4 
yintercept 
6 
4 
check point 


Some lines do not have both an xintercept and a yintercept.
â€¢ A horizontal line, other than the xaxis, has a yintercept, but
no xintercept.
For example, the horizontal line y = 6 has yintercept (0, 6), but no
xintercept.
â€¢ A vertical line, other than the yaxis, has an xintercept, but
no yintercept.
For example, the vertical line x = 2 has xintercept (2, 0), but no
yintercept.
