Geometry parallel and perpendicular lines worksheet

Parallel lines have the same slope. Perpendicular ones have slopes that multiply to negative one, which means flipping the fraction and changing the sign.



Sigma Prep · sigmaprep.io/worksheets Name Parallel and Perpendicular Lines Date Period Find the slope, or write the equation. Find the slope of a line perpendicular to $y = 3 x + 12$ Write the equation of the line through $(- 10, - 6)$ perpendicular to $y = \frac{5}{3} x - 2$ Find the slope of a line perpendicular to $y = - 6 x + 4$ Write the equation of the line through $(7, 1)$ perpendicular to $y = - 7 x + 3$ Find the slope of a line parallel to $y = 3 x - 10$ Write the equation of the line through $(- 12, 4)$ perpendicular to $y = 6 x - 4$ Find the slope of a line parallel to $y = 6 x - 8$ Write the equation of the line through $(3, 7)$ parallel to $y = 7 x - 3$ Find the slope of a line perpendicular to $y = 3 x + 2$ Write the equation of the line through $(- 8, 3)$ parallel to $y = - \frac{7}{4} x + 9$ Find the slope of a line perpendicular to $y = 2 x - 5$ Write the equation of the line through $(14, 6)$ perpendicular to $y = - \frac{7}{2} x + 5$ Find the slope of a line perpendicular to $y = 8 x - 2$ Write the equation of the line through $(- 4, 5)$ parallel to $y = \frac{7}{2} x - 5$ Find the slope of a line perpendicular to $y = - 3 x + 1$ Write the equation of the line through $(- 12, 6)$ perpendicular to $y = 6 x + 8$ Find the slope of a line perpendicular to $y = 9 x - 2$ Write the equation of the line through $(3, 3)$ parallel to $y = - \frac{7}{3} x - 9$ Find the slope of a line parallel to $y = - 7 x - 4$ Write the equation of the line through $(- 2, 5)$ perpendicular to $y = - \frac{1}{4} x + 4$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel and Perpendicular Lines

Date Period

Find the slope, or write the equation.

Find the slope of a line perpendicular to $y = 3 x + 12$
Write the equation of the line through $(- 10, - 6)$ perpendicular to $y = \frac{5}{3} x - 2$
Find the slope of a line perpendicular to $y = - 6 x + 4$
Write the equation of the line through $(7, 1)$ perpendicular to $y = - 7 x + 3$
Find the slope of a line parallel to $y = 3 x - 10$
Write the equation of the line through $(- 12, 4)$ perpendicular to $y = 6 x - 4$
Find the slope of a line parallel to $y = 6 x - 8$
Write the equation of the line through $(3, 7)$ parallel to $y = 7 x - 3$
Find the slope of a line perpendicular to $y = 3 x + 2$
Write the equation of the line through $(- 8, 3)$ parallel to $y = - \frac{7}{4} x + 9$
Find the slope of a line perpendicular to $y = 2 x - 5$
Write the equation of the line through $(14, 6)$ perpendicular to $y = - \frac{7}{2} x + 5$
Find the slope of a line perpendicular to $y = 8 x - 2$
Write the equation of the line through $(- 4, 5)$ parallel to $y = \frac{7}{2} x - 5$
Find the slope of a line perpendicular to $y = - 3 x + 1$
Write the equation of the line through $(- 12, 6)$ perpendicular to $y = 6 x + 8$
Find the slope of a line perpendicular to $y = 9 x - 2$
Write the equation of the line through $(3, 3)$ parallel to $y = - \frac{7}{3} x - 9$
Find the slope of a line parallel to $y = - 7 x - 4$
Write the equation of the line through $(- 2, 5)$ perpendicular to $y = - \frac{1}{4} x + 4$



Sigma Prep · sigmaprep.io/worksheets Name Parallel and Perpendicular LinesAnswer keyVersion 1 Date Period Find the slope, or write the equation. Find the slope of a line perpendicular to $y = 3 x + 12$ $- \frac{1}{3}$ Write the equation of the line through $(- 10, - 6)$ perpendicular to $y = \frac{5}{3} x - 2$ $y = - \frac{3}{5} x - 12$ Find the slope of a line perpendicular to $y = - 6 x + 4$ $\frac{1}{6}$ Write the equation of the line through $(7, 1)$ perpendicular to $y = - 7 x + 3$ $y = \frac{1}{7} x$ Find the slope of a line parallel to $y = 3 x - 10$ $3$ Write the equation of the line through $(- 12, 4)$ perpendicular to $y = 6 x - 4$ $y = - \frac{1}{6} x + 2$ Find the slope of a line parallel to $y = 6 x - 8$ $6$ Write the equation of the line through $(3, 7)$ parallel to $y = 7 x - 3$ $y = 7 x - 14$ Find the slope of a line perpendicular to $y = 3 x + 2$ $- \frac{1}{3}$ Write the equation of the line through $(- 8, 3)$ parallel to $y = - \frac{7}{4} x + 9$ $y = - \frac{7}{4} x - 11$ Find the slope of a line perpendicular to $y = 2 x - 5$ $- \frac{1}{2}$ Write the equation of the line through $(14, 6)$ perpendicular to $y = - \frac{7}{2} x + 5$ $y = \frac{2}{7} x + 2$ Find the slope of a line perpendicular to $y = 8 x - 2$ $- \frac{1}{8}$ Write the equation of the line through $(- 4, 5)$ parallel to $y = \frac{7}{2} x - 5$ $y = \frac{7}{2} x + 19$ Find the slope of a line perpendicular to $y = - 3 x + 1$ $\frac{1}{3}$ Write the equation of the line through $(- 12, 6)$ perpendicular to $y = 6 x + 8$ $y = - \frac{1}{6} x + 4$ Find the slope of a line perpendicular to $y = 9 x - 2$ $- \frac{1}{9}$ Write the equation of the line through $(3, 3)$ parallel to $y = - \frac{7}{3} x - 9$ $y = - \frac{7}{3} x + 10$ Find the slope of a line parallel to $y = - 7 x - 4$ $- 7$ Write the equation of the line through $(- 2, 5)$ perpendicular to $y = - \frac{1}{4} x + 4$ $y = 4 x + 13$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel and Perpendicular LinesAnswer keyVersion 1

Date Period

Find the slope, or write the equation.

Find the slope of a line perpendicular to $y = 3 x + 12$ $- \frac{1}{3}$
Write the equation of the line through $(- 10, - 6)$ perpendicular to $y = \frac{5}{3} x - 2$ $y = - \frac{3}{5} x - 12$
Find the slope of a line perpendicular to $y = - 6 x + 4$ $\frac{1}{6}$
Write the equation of the line through $(7, 1)$ perpendicular to $y = - 7 x + 3$ $y = \frac{1}{7} x$
Find the slope of a line parallel to $y = 3 x - 10$ $3$
Write the equation of the line through $(- 12, 4)$ perpendicular to $y = 6 x - 4$ $y = - \frac{1}{6} x + 2$
Find the slope of a line parallel to $y = 6 x - 8$ $6$
Write the equation of the line through $(3, 7)$ parallel to $y = 7 x - 3$ $y = 7 x - 14$
Find the slope of a line perpendicular to $y = 3 x + 2$ $- \frac{1}{3}$
Write the equation of the line through $(- 8, 3)$ parallel to $y = - \frac{7}{4} x + 9$ $y = - \frac{7}{4} x - 11$
Find the slope of a line perpendicular to $y = 2 x - 5$ $- \frac{1}{2}$
Write the equation of the line through $(14, 6)$ perpendicular to $y = - \frac{7}{2} x + 5$ $y = \frac{2}{7} x + 2$
Find the slope of a line perpendicular to $y = 8 x - 2$ $- \frac{1}{8}$
Write the equation of the line through $(- 4, 5)$ parallel to $y = \frac{7}{2} x - 5$ $y = \frac{7}{2} x + 19$
Find the slope of a line perpendicular to $y = - 3 x + 1$ $\frac{1}{3}$
Write the equation of the line through $(- 12, 6)$ perpendicular to $y = 6 x + 8$ $y = - \frac{1}{6} x + 4$
Find the slope of a line perpendicular to $y = 9 x - 2$ $- \frac{1}{9}$
Write the equation of the line through $(3, 3)$ parallel to $y = - \frac{7}{3} x - 9$ $y = - \frac{7}{3} x + 10$
Find the slope of a line parallel to $y = - 7 x - 4$ $- 7$
Write the equation of the line through $(- 2, 5)$ perpendicular to $y = - \frac{1}{4} x + 4$ $y = 4 x + 13$

How to do these

Find the slope of a line perpendicular to $y = 3 x - 2$

The slope is 3, which is 3 over 1.
Flip it to 1 over 3.
Change the sign.

The answer is $- \frac{1}{3}$ .

Where students go wrong

Flipping without negating, or negating without flipping. Both are needed, and the check is that the two slopes multiply to exactly -1.

Also called negative reciprocal, slopes of parallel lines or perpendicular slope.

What you can put on this worksheet

Slopes of parallel and perpendicular lines: Find the slope of a line parallel to $y = 3 x - 6$ → $3$
The equation through a point, parallel or perpendicular: Write the equation of the line through $(0, - 4)$ perpendicular to $y = 3 x + 1$ → $y = - \frac{1}{3} x - 4$

Questions about these worksheets

Yes. Every parallel and perpendicular lines sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the parallel and perpendicular lines questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: slopes of parallel and perpendicular lines and the equation through a point, parallel or perpendicular. Tick as many as you want and set how many of each, or let it spread them evenly.

Flipping without negating, or negating without flipping. Both are needed, and the check is that the two slopes multiply to exactly -1.

Geometry parallel and perpendicular lines worksheet

Parallel and Perpendicular Lines

Parallel and Perpendicular LinesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these parallel and perpendicular lines worksheets free?+

Do the parallel and perpendicular lines worksheets come with an answer key?+

Are these parallel and perpendicular lines worksheets printable?+

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Is this a free alternative to Kuta Software for parallel and perpendicular lines?+

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What do students get wrong with parallel and perpendicular lines?+