Start free
Back to the lesson

Parallel and perpendicular lines GCSE lesson: gradients m and −1/m

Name: ____________________ Date: ____________________

Show your working. Check every root by substitution and label your sketches.

Parallel and perpendicular lines: practice

Show your working on paper. Write fractions with /, such as -1/3, and negative numbers with a minus sign. The stretch is optional.

Diagnostic question: choose and explain

  1. A line has gradient −⅔. What is the gradient of a line perpendicular to it?
    1. 3/2
    2. −3/2
    3. 2/3
    4. −2/3

Practice questions

  1. A line parallel to y = 5x − 2 has gradient ___
  2. A line perpendicular to y = 5x − 2 has gradient ___
  3. 2y = 6x + 1. A line perpendicular to it has gradient ___
  4. y = 4 − ½x. What is the gradient of a line perpendicular to it?
  5. Which pair of lines is perpendicular?
    1. y = 2x + 3 and y = −2x + 1
    2. y = 2x + 3 and y = ½x − 4
    3. y = 2x + 3 and y = 3 − ½x
    4. y = 2x + 3 and y = 2x − 1
  6. Line A goes through (0, 1) and (2, 5). Line B goes through (0, 3) and (4, 1). Are they perpendicular?
    1. Yes
    2. No
  7. The line perpendicular to y = 2x + 1 through (4, 3) is y = ___x + ___
  8. The line parallel to y = 3x − 2 through (1, 7) is y = 3x + ___
  9. A line goes through (1, 2) and (5, 4). A line perpendicular to it has gradient ___
  10. Stretch: the line through (1, 6) perpendicular to y = ⅓x + 1 meets the x-axis at x = ___

Support: For question 3: divide every term by 2 first, so the equation starts y = … . Then flip the gradient and change its sign. Check: the two gradients multiply to −1.

Parallel and perpendicular lines: exit

Two equations and one sentence are enough.

  1. L is the line y = 4x − 3. Write the equation of the line parallel to L through (0, 2), and of the line perpendicular to L through (0, 2). Say how you know each one.

Exit check

One parallel and one perpendicular line through the same point show who has both rules.

L is y = 4x − 3. Write the line parallel to L through (0, 2), and the line perpendicular to L through (0, 2).

Parallel and perpendicular lines: gradients and lines

Show your working. Rearrange into y = mx + c before reading a gradient. Check every perpendicular pair: the gradients multiply to −1.

1. Write the gradient of a line parallel to y = 6x − 1, and of a line perpendicular to it.

2. Write the gradient of a line perpendicular to y = −⅗x + 2.

3. Write 3x + 2y = 6 in the form y = mx + c. Then write the gradient of a line perpendicular to it.

4. Find the equation of the line perpendicular to y = 2x − 5 that goes through (6, 1).

5. Show that y = 3x + 1 and x + 3y = 12 are perpendicular.

6. A is (0, 1) and B is (2, 5). Find the equation of the line through B that is perpendicular to AB.

SKRM Learn · Original teaching resource · Free to use with your students.