TOPIC

Parallel line equation

MY PROGRESS

Pug Score

0%

Best Streak

0 in a row

Study Points

+0

Overview

Practice

Watch

Read

Next Steps

Get Started

Get unlimited access to all videos, practice problems, and study tools.

Try Now
Unlimited practice
Full videos

Back to Menu

Topic Progress

Pug Score

0%

Videos Watched

0/0

Best Practice

No score

Read

Not viewed

Best Streak

0 in a row

Study Points

+0

Read

Parallel Line Equations

Two lines are parallel when they have the exact same slope but different y-intercepts, so they never cross. Learn to identify parallel lines from their equations and write the equation of a line parallel to a given one, with a worked example.

What makes lines parallel

Two lines are parallel if they have the exact same slope but different y-intercepts. Same slope means they rise and run at the same rate, so they never get closer together or farther apart — and never cross.

Worked example

The lines y = 2x + 1 and y = 2x − 2 both have a slope of 2. Since the slopes match but the y-intercepts (1 and −2) differ, the lines are parallel.

Parallel lines share the same slope The lines y = 2x + 1 and y = 2x - 2 both have a slope of 2, so they are parallel and never meet, even though they cross the y-axis at different points. x y y = 2x + 1 y = 2x − 2
y = 2x + 1 and y = 2x − 2 are parallel: same slope, different y-intercepts.

Writing the equation of a parallel line

To write an equation for a line parallel to a given one, keep the same slope and change only the y-intercept (or solve for it using a given point). This is the mirror image of finding a perpendicular line, which instead uses the negative reciprocal of the slope. It depends on being able to read the slope from slope-intercept form or compute it directly with the slope formula.

Related lessons