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Parallel line equation

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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.

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