# Intercept Form

How to solve intercept form problems (linear equations): formula, proof, examples, and their solutions.

## 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*x*-intercept, *y*-intercept

## Proof

The *x*-intercept is (*a*, 0).

And the *y*-intercept is (0, *b*).

The change of *x* is *a* - 0 = *a*.

And the change of *y* is 0 - *b* = -*b*.

Then the slope of the line is*m* = -*b*/*a*.

Slope of a line

The slope of the line is -*b*/*a*.

And the *y*-intercept is *b*.

Then the linear equation in slope-intercept form

is *y* = [-*b*/*a*]*x* + *b*.

Divide both sides by *b*.

Move -*x*/*a* to the left side.

Then *x*/*a* + *y*/*b* = 1.

## Example 1

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

in slope-intercept form.

Move *x*/(-3) to the right side.

Multiply 2 on both sides.

Then *y* = (2/3)*x* + 2.

## Example 2

To find the intercepts clearly,

change -*y*/4 to *y*/(-4):*x*/5 + *y*/(-4) = 1.

The *x*-intercept is 5.

And the *y*-intercept is -4.

To graph the linear equation:

Point the *x*-intercept on the *x*-axis: (5, 0).

And point the *y*-intercept on the *y*-axis: (0, -4).

Draw a line that passes through these two intercepts.