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Parallel line equation

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Algebra I

31. CC.HSF.LE.A.3

31.1 Parallel line equation

Parallel Line Equations

Parallel lines share the same slope but have different y-intercepts, so they never cross.

What You'll Learn

Parallel lines have the same slope but different y-intercepts.

Same slope means the lines rise and run at the same rate and never meet.

y = 2x + 1 and y = 2x - 2 are parallel: both have slope 2.

To write a parallel line's equation, keep the slope and change the y-intercept.

Perpendicular lines use the negative reciprocal slope instead.

What You'll Practice

Finding slopes from graphed lines and writing parallel equations

Calculating slopes of horizontal and vertical lines

Converting standard form equations to slope-intercept form

Writing new parallel line equations through specific points

Solving for unknowns when parallel conditions are given

Why This Matters

Understanding parallel line equations is essential for algebra, geometry, and coordinate graphing. You'll use this skill to analyze geometric relationships, solve systems of equations, and work with linear models in physics and engineering applications.

Before You Start — Make Sure You Can:

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)Slope intercept form: y = mx + b General form: Ax + By + C = 0 Point-slope form: \(y - y_1 = m (x - x_1)\)

This Unit Includes

7 Video lessons

Practice exercises

Learning resources

Skills

Parallel Lines

Slope

Linear Equations

Slope-Intercept Form

Standard Form

Graphing

Coordinate Geometry

OH Curriculum Aligned