Parallel and Perpendicular Lines

ACT Math · Axiom Academy

LESSON Parallel and Perpendicular Lines Two lines, one number each — the slope tells you everything about how they relate, and the ACT tests it constantly. 1. Parallel Lines Share One Slope Parallel lines never meet, no matter how far you extend them — and the reason is entirely about slope. If two lines climb at the exact same rate , they can never converge or drift apart differently, so they stay the same distance apart forever. Parallel lines have EQUAL slopes ...but DIFFERENT y-intercepts (otherwise they're the same line) Worked example: write a line parallel to y = 3x + 2 through (2, 1) Same slope as the original ( m=3 ), a genuinely different intercept ( ), and it passes through (2,1) : 3(2) - 5 = 1 . ✓︎ 2. Perpendicular Lines Flip and Flip the Sign Perpendicular lines cross at a true 90° angle. That specific angle forces a precise slope relationship: the second line's slope is the negative reciprocal of the first — flip the fraction upside down, then flip the sign. Equivalently: the two slopes multiply to -1 Flip to , then negate: perpendicular slope . 3. Writing the Line Through a Given Point The most common ACT setup: you're handed a line and a point, and asked to write the equation of a new line through that point — either parallel or perpendicular to the original. Double-check the perpendicular answer

This is the written version of the interactive lesson above. See the full ACT Math course.