# Parallel Line Equation

How to find the linear equation that is parallel to the given line: definition, 1 example, and its solution.

## Definition

Parallel Lines are the lines that have the same slope

and have the different y-intercepts.

## Symbol

The triangle symbols are used

to show that the lines are parallel.

## ExampleLine Parallel to y = 3x + 4

Solution

Solution (Detail)

It says

the line is parallel to y = 3x + 4.

So the slope of the line you're looking for is

m = 3.

The slope, m, is 3.

And the line passes through (1, -2).

So the linear equation in point-slope form is

y = 3(x - 1) - 2.

Change the linear equation to slope-intercept form.

Then y = 3x - 5.

So

y = 3x - 5

is the answer.

Graph

The left line is the given line y = 3x + 4.

And the right line is the answer y = 3x - 5.

y = 3x - 5 is parallel to y = 3x + 4.

And it passes through (1, -2).