Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
MathsAges 16-18

Gradient of a line

Calculate the gradient of a straight line segment joining two coordinate points using rise divided by run. Review suitability for your learners before teaching.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (3, 8) and (9, 38).

    3 · 8 · 9 · 38 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 21).

    5 · 9 · 11 · 21 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 6) and (10, 22).

    8 · 6 · 10 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 6) and (2, 8).

    1 · 6 · 2 · 8 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 8) and (11, 11).

    8 · 8 · 11 · 11 · Gradient of a line

  6. 6. Find the gradient of the line passing through (7, 9) and (8, 10).

    7 · 9 · 8 · 10 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 7) and (10, 16).

    7 · 7 · 10 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 1) and (2, 9).

    1 · 1 · 2 · 9 · Gradient of a line

  9. 9. Find the gradient of the line passing through (1, 7) and (7, 37).

    1 · 7 · 7 · 37 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 38).

    6 · 2 · 10 · 38 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 35).

    2 · 5 · 8 · 35 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 8) and (5, 28).

    1 · 8 · 5 · 28 · Gradient of a line
12 questions · Seed 104747 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (3, 8) and (9, 38).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 8) ÷ (9 − 3) = 30 ÷ 6 = 5.

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 21).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (11 − 5) = 12 ÷ 6 = 2.

  3. 3. Find the gradient of the line passing through (8, 6) and (10, 22).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 6) ÷ (10 − 8) = 16 ÷ 2 = 8.

  4. 4. Find the gradient of the line passing through (1, 6) and (2, 8).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 6) ÷ (2 − 1) = 2 ÷ 1 = 2.

  5. 5. Find the gradient of the line passing through (8, 8) and (11, 11).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 8) ÷ (11 − 8) = 3 ÷ 3 = 1.

  6. 6. Find the gradient of the line passing through (7, 9) and (8, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 9) ÷ (8 − 7) = 1 ÷ 1 = 1.

  7. 7. Find the gradient of the line passing through (7, 7) and (10, 16).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 7) ÷ (10 − 7) = 9 ÷ 3 = 3.

  8. 8. Find the gradient of the line passing through (1, 1) and (2, 9).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 1) ÷ (2 − 1) = 8 ÷ 1 = 8.

  9. 9. Find the gradient of the line passing through (1, 7) and (7, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (7 − 1) = 30 ÷ 6 = 5.

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 38).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 2) ÷ (10 − 6) = 36 ÷ 4 = 9.

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 5) ÷ (8 − 2) = 30 ÷ 6 = 5.

  12. 12. Find the gradient of the line passing through (1, 8) and (5, 28).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 8) ÷ (5 − 1) = 20 ÷ 4 = 5.

12 questions · Seed 104747 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (3, 8) and (9, 38).

    3 · 8 · 9 · 38 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 21).

    5 · 9 · 11 · 21 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 6) and (10, 22).

    8 · 6 · 10 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 6) and (2, 8).

    1 · 6 · 2 · 8 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 8) and (11, 11).

    8 · 8 · 11 · 11 · Gradient of a line

  6. 6. Find the gradient of the line passing through (7, 9) and (8, 10).

    7 · 9 · 8 · 10 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 7) and (10, 16).

    7 · 7 · 10 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 1) and (2, 9).

    1 · 1 · 2 · 9 · Gradient of a line

  9. 9. Find the gradient of the line passing through (1, 7) and (7, 37).

    1 · 7 · 7 · 37 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 38).

    6 · 2 · 10 · 38 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 35).

    2 · 5 · 8 · 35 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 8) and (5, 28).

    1 · 8 · 5 · 28 · Gradient of a line
12 questions · Seed 104747 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (3, 8) and (9, 38).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 8) ÷ (9 − 3) = 30 ÷ 6 = 5.

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 21).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (11 − 5) = 12 ÷ 6 = 2.

  3. 3. Find the gradient of the line passing through (8, 6) and (10, 22).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 6) ÷ (10 − 8) = 16 ÷ 2 = 8.

  4. 4. Find the gradient of the line passing through (1, 6) and (2, 8).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 6) ÷ (2 − 1) = 2 ÷ 1 = 2.

  5. 5. Find the gradient of the line passing through (8, 8) and (11, 11).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 8) ÷ (11 − 8) = 3 ÷ 3 = 1.

  6. 6. Find the gradient of the line passing through (7, 9) and (8, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 9) ÷ (8 − 7) = 1 ÷ 1 = 1.

  7. 7. Find the gradient of the line passing through (7, 7) and (10, 16).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 7) ÷ (10 − 7) = 9 ÷ 3 = 3.

  8. 8. Find the gradient of the line passing through (1, 1) and (2, 9).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 1) ÷ (2 − 1) = 8 ÷ 1 = 8.

  9. 9. Find the gradient of the line passing through (1, 7) and (7, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (7 − 1) = 30 ÷ 6 = 5.

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 38).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 2) ÷ (10 − 6) = 36 ÷ 4 = 9.

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 5) ÷ (8 − 2) = 30 ÷ 6 = 5.

  12. 12. Find the gradient of the line passing through (1, 8) and (5, 28).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 8) ÷ (5 − 1) = 20 ÷ 4 = 5.

12 questions · Seed 104747 · Age guidance, not curriculum certification