Equations of Parallel and Perpendicular Lines

Write linear equations with a given point and relationship.

Lesson 5 of 53 parts Practice Flashcards

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Slope-Intercept Form

Objective: Find slope and intercept from y=mx+b.

In y=mx+b, m is slope and b is the y-intercept. Parallel lines have the same slope but distinct intercepts in this form.

The line y equals 2x plus 2 crosses the y-axis at 2 and rises 2 for every 1 unit of run.

Formulas

$y=mx+b$

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Slope-Intercept Form

Objective: Find slope and intercept from y=mx+b.

In y=mx+b, m is slope and b is the y-intercept. Parallel lines have the same slope but distinct intercepts in this form.

Formulas

$y=mx+b$

Point-Slope Form

Objective: Write a line from a point and slope.

A line of slope m through (x₁,y₁) satisfies y−y₁=m(x−x₁). This can be rearranged into slope-intercept form.

Formulas

$y-y_1=m(x-x_1)$

Related Line Equations

Objective: Find equations of parallel and perpendicular lines through a point.

For nonvertical lines, preserve slope to create a parallel line; use the negative reciprocal for a perpendicular line. Handle horizontal and vertical lines separately.

Two teal parallel lines with slope one half and a red line of slope negative two meeting one of them at a right angle.

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