# Slope-Intercept Form

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

## Formula

The linear equation in slope-intercept form is*y* = *mx* + *b*.*m*: Slope of the line*b*: *y*-intercept of the line

Slope of a line*x*-intercept, *y*-intercept

## Proof

Think of a slope between (0, *b*) and (*x*, *y*).

(*x*, *y*) is the point on the line.

The change of *x* is, *x* - 0, [*x*].

And the change of *y* is [*y* - *b*].

Then the slope of the line is (*y* - *b*)/*x*.

Then set (*y* - *b*)/*x* = *m*.

Multiply *x* on both sides.

Move -*b* to the right side.

Then *y* = *mx* + *b*.

## Example 1

The *y*-intercept is -1.

And the slope, *m*, is 2/1 = 2.

So the linear equation is *y* = 2*x* - 1.

## Example 2

The slope is 3.

And the *y*-intercept is -1.

So start from the *y*-intercept: -1.

The slope is 3.

So move 1 unit to the right

and move 3 units upward.

Let's call this point the 'endpoint'.

Draw a line that passes through

the *y*-intercept and the endpoint.

This line is the answer.

## Example 3

Slope-intercept form is *y* = *mx* + *b*.

There's only *y* term on the left side.

So move the *x* term, 5*x*, to the right side.

Divide both sides by -3.

Then *y* = (5/3)*x* - 2.

This linear equation is in slope-intercept form.

So this is the answer.

Let's graph *y* = (5/3)*x* - 2

on the coordinate plane.

Start from the *y*-intercept: -2.

The slope is 5/3.

So move 3 unit to the right

and move 5 units upward.

Let's call this point the 'endpoint'.

Draw a line that passes through

the *y*-intercept and the endpoint.