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.