Parallel and Perpendicular Lines
Practice the slope rules for parallel and perpendicular lines and how to write their equations.
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Questions Covered in This Set
12 cards to master
What is true about the slopes of parallel lines?
They are equal (m₁ = m₂), but the y-intercepts differ.
What is true about the slopes of perpendicular lines?
They are negative reciprocals: m₂ = -1/m₁, so m₁·m₂ = -1.
Mental recipe for finding a perpendicular slope
Flip the fraction, flip the sign (e.g., 2/3 → -3/2).
Slope perpendicular to y = (7/2)x - 1
-2/7
Line ℓ passes through (0,1) and (4,3). Perpendicular slope?
Slope of ℓ = 1/2, so perpendicular slope = -2.
Find the line perpendicular to 3x + 5y = 10 through (3, -2).
Slope of given line = -3/5, perpendicular = 5/3; y = (5/3)x - 7.
What is perpendicular to a horizontal line like y = 4?
A vertical line like x = 7 (undefined slope); memorize this pair since the reciprocal rule fails.
Same slope and same y-intercept means...
The lines are identical — infinitely many solutions as a system.
Same slope, different y-intercept means...
Parallel lines — no solution as a system.
If kx + 4y = 9 is perpendicular to y = 2x + 1, find k.
y = -(k/4)x + 9/4, need -k/4 = -1/2, so k = 2.
How do you check a perpendicular slope answer?
Multiply the two slopes; the product must be exactly -1.
Write the line through (-1, 4) parallel to y = (1/3)x
y - 4 = (1/3)(x + 1) → y = (1/3)x + 13/3
