Parallel and Perpendicular Lines Worksheet PDF With a Drawn Answer Key

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Parallel and Perpendicular Lines

Name Date Score / 19

Are the two lines parallel, perpendicular or neither? Count the rise and run of each line, then mark one.

  1. 1.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    parallelperpendicularneither

  2. 2.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    parallelperpendicularneither

  3. 3.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    parallelperpendicularneither

Find the slope of each line where it is not given. Then mark the lines parallel, perpendicular or neither.

  1. 4.

    A: y = 4x − 9
    B: y = −1⁄4x + 8

    slope of A slope of B

    parallelperpendicularneither

  2. 5.

    Line A: (−2, 2) and (0, 1)
    Line B: (3, −2) and (4, −4)

    slope of A slope of B

    parallelperpendicularneither

  3. 6.

    Slopes −3⁄2 and −3⁄2

    parallelperpendicularneither

Write the slope of a line parallel to each line, and the slope of a line perpendicular to it.

  1. 7.

    y = 3x + 1

    parallel perpendicular

  2. 8.

    y = −x − 4

    parallel perpendicular

  3. 9.

    y = 4x − 6

    parallel perpendicular

Write the equation of the line through the point that is parallel or perpendicular to the given line, in the form y = mx + b.

  1. 10.

    Through (8, −6), perpendicular to y = 2x − 9

    y =

  2. 11.

    Through (2, 6), parallel to y = 5x − 3

    y =

  3. 12.

    Through (−5, −7), perpendicular to y = −5⁄3x + 2

    y =

Sheet 52UZUJ · Made at homeroomtools.com

Answer key: Parallel and Perpendicular Lines

  1. 1. parallel: slopes 1⁄5 and 1⁄5

    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

  2. 2. perpendicular: slopes −1 and 1

    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

  3. 3. neither: slopes −1⁄5 and 1⁄5

    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

  1. 4. slopes 4 and −1⁄4: perpendicular

    xy−10−55100−10−5510

  2. 5. slopes −1⁄2 and −2: neither

    xy−10−55100−10−5510

  3. 6. slopes −3⁄2 and −3⁄2: parallel

    xy−10−55100−10−5510

  1. 7. parallel 3, perpendicular −1⁄3

  2. 8. parallel −1, perpendicular 1

  3. 9. parallel 4, perpendicular −1⁄4

  1. 10. y = −1⁄2x − 2

    xy−10−55100−10−5510

  2. 11. y = 5x − 4

    xy−10−55100−10−5510

  3. 12. y = 3⁄5x − 4

    xy−10−55100−10−5510

Sheet 52UZUJ · answer key · Made at homeroomtools.com

Scroll the preview to see every page. Paper copies fit US Letter and A4 and need no colour ink.

12 problems on one page, plus the answer key. Sheet 52UZUJ.

On the sheet
Problems
Equations

Next step Next: where two lines cross, systems by graphingShaky on slope? Review every way to find it

Slope and line facts behind every answer key

Show the table

Every line on these sheets goes through grid points with whole-number coordinates, so a slope can be counted off the graph square by square. The key is worked out with whole-number arithmetic and every slope is given in lowest terms.

IdeaWhat it says
Sloperise over run: the change in y divided by the change in x, m = (y₂ − y₁) ÷ (x₂ − x₁)
Slope-intercept formy = mx + b, where m is the slope and b is the y-intercept, the point (0, b) where the line crosses the y-axis
Positive and negativea line that climbs from left to right has a positive slope; one that falls has a negative slope
Zero slopea horizontal line, y = b: it rises by nothing, however far it runs
Undefined slopea vertical line, x = a: its run is 0, and nothing can be divided by 0
From a tablepick any two rows: the difference of the y values over the difference of the x values, in the same order
Standard formAx + By = C. Put y = 0 to find the x-intercept, C ÷ A, and x = 0 to find the y-intercept, C ÷ B
From a point and a slopeput the point into y = mx + b and solve for b: b = y − mx

A short code sits at the foot of every sheet and of its answer key, so loose pages can be matched. The share link rebuilds that sheet, number for number: a key printed next week still fits the copies handed out today.

How it works

This parallel and perpendicular lines worksheet opens with 12 problems: three pairs of drawn lines to classify, three pairs given as equations, points or slopes, three slopes to find and three equations to write.

Read the full guide

Parallel and perpendicular worksheet, four tasks

Parallel or perpendicular, from a graph: two drawn lines; count rise and run, then mark parallel, perpendicular or neither. Parallel or perpendicular, without a graph: the same choice from two equations, four points or two slopes. Parallel and perpendicular slopes: a slopes of parallel and perpendicular lines worksheet, one line given and two slopes to write. Parallel or perpendicular line through a point: an equations of parallel and perpendicular lines worksheet, such as through (2, 6), parallel to y = 5x − 3.

The two slope rules

Parallel lines have the same slope. Perpendicular lines have slopes that multiply to −1, so each is the negative reciprocal of the other: 4 and −1/4.

  • About a third of the pairs are neither, with slopes that look close, such as −1/5 and 1/5.
  • For a parallel and perpendicular slopes worksheet with no graphs, light only the third task; 16 problems fit one page.
  • Other forms too prints some lines as 3x + 2y = 4, so students solve for y before comparing.

Questions and answers

How do I get a parallel and perpendicular lines worksheet PDF?

Press Print and choose Save as PDF in your browser's print window. The opening sheet is one page of 12 problems, then the answer key, which gives both slopes for every pair and redraws each graph.

How do you tell if two lines are parallel, perpendicular or neither?

Find both slopes. Equal slopes with different y-intercepts mean parallel lines. Slopes whose product is −1, such as 2 and −1/2, mean perpendicular lines. Anything else is neither.

What is the slope of a line perpendicular to y = 3x + 1?

It is −1/3. Flip the slope 3 to get 1/3, then change its sign. A parallel line keeps the slope 3. The key prints both: parallel 3, perpendicular −1/3.

How do you write the equation of a parallel line through a point?

Keep the slope and solve for b. Through (2, 6), parallel to y = 5x − 3: 6 = 5 × 2 + b, so b = −4 and the line is y = 5x − 4.

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