Any equation that relates the first power of *x* to the first power of *y* produces a straight line on an *x*-*y* graph. The standard form of such an equation is *Ax* + *By* + *C* = 0 or *Ax* + *By* = *C*. When you rearrange this equation to get y by itself on the left side, it takes the form *y* = *mx* +*b*. This is called slope intercept form because m is equal to the slope of the line, and *b* is the value of *y* when *x* = 0, which makes it the *y*-intercept. Converting from slope intercept form to standard form takes little more than basic arithmetic.

#### TL;DR (Too Long; Didn't Read)

To convert from slope intercept form *y* = *mx* + *b* to standard form *Ax* + *By* + *C* = 0, let *m* = *A*/*B*, collect all terms on the left side of the equation and multiply by the denominator *B* to get rid of the fraction.

## The General Procedure

An equation in slope intercept form has the basic structure

## Subtract mx From Both Sides

## Subtract b From Both Sides (Optional)

## Rearrange to Put the x Term First

## Let the Fraction A/B Represent m

## Multiply Both Sides of the Equation by the Denominator B

## Let Bb = C

If *m* is an integer, then *B* will equal 1.

## Examples:

(1) - The equation of a line in slope intercept form is:

What is the equation in standard form?

## Subtract 1/2 x From Both Sides of the Equation

## Subtract 5 From Both Sides

## Multiply Both Sides by the Denominator of the Fraction

## Rearrange to Put x as the First Term

You can leave the equation like this, but if you prefer to make *x* positive, multiply both sides by -1:

or

(2) - The slope of a line is -3/7 and the y-intercept is 10. What is the equation of the line in standard form?

The slope intercept form of the line is

Following the procedure outlined above: