Parallel lines have the same slope. Perpendicular lines have slopes that multiply to −1. That is the whole coordinate test. Slope itself is in slope on ACT Math, and the plane is in coordinate geometry.
Parallel
y = 2x + 1 and y = 2x − 4 are parallel. Same slope, different intercepts, so they never meet. If a question asks for a line parallel to y = 2x + 1 through (3, 5), keep slope 2 and solve 5 = 2(3) + b. The new line is y = 2x − 1.
Perpendicular
The slope perpendicular to 2 is −1/2. Flip the fraction and change the sign. A slope of −3/4 is perpendicular to 4/3. Horizontal and vertical lines are perpendicular too: slope 0 and an undefined slope. Do not try to “flip” undefined.
Angle facts that are not about slope — vertical angles, transversals — are in lines and angles. The formula list is in ACT Math formulas.
The bottom line
Copy the slope for parallel. Flip it and change the sign for perpendicular.
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