# 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 = 2x - 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.

## Example 3

Slope-intercept form is y = mx + b.

There's only y term on the left side.

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

Divide both sides by -3.

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

This linear equation is in slope-intercept form.