Intercept Form

How to write and graph a linear equation in intercept form: formula, 2 examples, and their solutions.

Formula

Formula

The linear equation in intercept form is
x/a + y/b = 1.

a: x-intercept of the line

b: y-intercept of the line

Example 1

Example

Solution

The x-intercept is -3.
And the y-intercept is 2.

Then the linear equation in intercept form is
x/(-3) + y/2 = 1.

Change the linear equation to slope-intercept form.

Move x/(-3) to the right side.
Then y/2 = x/3 + 1.

Multiply 2 to both sides.
Then y = (2/3)x + 2.

So y = (2/3)x + 2 is the answer.

Graph

This is the graph of the linear equation
x/(-3) + y/2 = 1.

The x-intercept is -3.
And the y-intercept is 2.

Example 2

Example

Solution

To see the y-intercept clearly,
change -y/4 to +y/(-4).

Then x/5 + y/(-4) = 1.
This is in intercept form.

The x-intercept is 5.
And the y-intercept is -4.

See x/5 + y/(-4) = 1.

The x-intercept is 5.
So point the x-intercept 5
on the coordinate plane.

The y-intercept is -4.
So point the y-intercept -4
on the coordinate plane.

Draw a line that passes through
the x-intercept and the y-intercept.

This is the graph of the linear equation
x/5 + y/(-4) = 1.