Parallel lines have equal slopes; perpendicular slopes are negative reciprocals. These free printable worksheets hand you a line and a point and ask for the new line — which is the only version of the rule a student has to actually use.
If they get stuck
The answer key prints on a separate page.
Knowing the criterion and using it are different things, and the gap is one step wide. A sheet that asks “what is the slope of a line perpendicular to y = 3x?” tests a definition; these sheets ask for the whole equation through a given point, so the slope has to be found, then turned over or kept, then put back together with an intercept. That last part is `y = mx + b` again, which is why this page sits just after writing the equation of a line.
The perpendicular questions give their line in standard form — x + 4y = 4 rather than y = −¼x + 1 — and that is deliberate. A perpendicular slope is a reciprocal, so one side of the pair is always a fraction; putting the fraction in the GIVEN line, where it never has to be written down, keeps the answer whole. Rearranging the standard form to read its slope is the extra step, and it is useful work rather than a chore.
Write the equation of the line (3, 2), ⊥ x − y = −2
