# Slope-Intercept Form

How to write and graph a linear equation in slope-intercept form: formula, 3 examples, and their solutions.

## Formula

### Formula

The linear equation in slope-intercept form is

y = mx + b.

m: Slope of the line

b: y-intercept of the line

## Example 1

### Example

### Solution

The slope is 2.

And the y-intercept is 1.

Then the linear equation in slope-intercept form is

y = 2x + 1.

### Graph

This is the graph of the linear equation y = 2x + 1.

The slope is 2.

And the y-intercept is 1.

## Example 2

### Example

### Solution

y = 3x - 2 is in slope-intercept form.

The y-intercept is -2.

So point the y-intercept -2

on the coordinate plane.

See y = 3x - 2 again.

The slope is 3. (= 3/1)

So move 1 unit to the right

and move 3 units upward.

Mark this endpoint.

Draw a line that passes through

the y-intercept and the marked endpoint.

This is the graph of the linear equation

y = 3x - 2.

## Example 3

### Example

5x + 3y = 6 is a linear equation in standard form:

Ax + by = C.

Let's see how to change this standard form to slope-intercept form.

### Solution

Move the x term, 5x, to the right side.

Then 3y = -5x + 6.

Divide both sides by 3.

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

See y = (-5/3)x + 2.

The slope is (-5/3).

The y-intercept is 2.

So y = (-5/3)x + 2 is the slope-intercept form of the linear equation.

### Graph

This is the graph of the linear equation y = (-5/3)x + 2:

the slope-intercept form of 5x + 3y = 6.

The slope is -5/3.

And the y-intercept is 2.