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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.

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Age band:Ages 13-15Ages 16-18

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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 (4, 8) and (5, 10).

    4 · 8 · 5 · 10 · Gradient of a line

  2. 2. Find the gradient of the line passing through (1, 8) and (4, 23).

    1 · 8 · 4 · 23 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 1) and (5, 13).

    1 · 1 · 5 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (5, 4) and (6, 6).

    5 · 4 · 6 · 6 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 9) and (7, 44).

    2 · 9 · 7 · 44 · Gradient of a line

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

    4 · 4 · 8 · 8 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 7) and (7, 27).

    3 · 7 · 7 · 27 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 4) and (11, 40).

    7 · 4 · 11 · 40 · Gradient of a line

  9. 9. Find the gradient of the line passing through (6, 7) and (11, 32).

    6 · 7 · 11 · 32 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 4) and (13, 46).

    7 · 4 · 13 · 46 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 10) and (11, 22).

    5 · 10 · 11 · 22 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 7) and (10, 19).

    4 · 7 · 10 · 19 · Gradient of a line
12 questions · Seed 42 · 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 (4, 8) and (5, 10).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 8) ÷ (5 − 4) = 2 ÷ 1 = 2.

  2. 2. Find the gradient of the line passing through (1, 8) and (4, 23).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 8) ÷ (4 − 1) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (1, 1) and (5, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (5 − 1) = 12 ÷ 4 = 3.

  4. 4. Find the gradient of the line passing through (5, 4) and (6, 6).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 4) ÷ (6 − 5) = 2 ÷ 1 = 2.

  5. 5. Find the gradient of the line passing through (2, 9) and (7, 44).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (44 − 9) ÷ (7 − 2) = 35 ÷ 5 = 7.

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

    1

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

  7. 7. Find the gradient of the line passing through (3, 7) and (7, 27).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 7) ÷ (7 − 3) = 20 ÷ 4 = 5.

  8. 8. Find the gradient of the line passing through (7, 4) and (11, 40).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (40 − 4) ÷ (11 − 7) = 36 ÷ 4 = 9.

  9. 9. Find the gradient of the line passing through (6, 7) and (11, 32).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (32 − 7) ÷ (11 − 6) = 25 ÷ 5 = 5.

  10. 10. Find the gradient of the line passing through (7, 4) and (13, 46).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 4) ÷ (13 − 7) = 42 ÷ 6 = 7.

  11. 11. Find the gradient of the line passing through (5, 10) and (11, 22).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 10) ÷ (11 − 5) = 12 ÷ 6 = 2.

  12. 12. Find the gradient of the line passing through (4, 7) and (10, 19).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (10 − 4) = 12 ÷ 6 = 2.

12 questions · Seed 42 · 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 (4, 8) and (5, 10).

    4 · 8 · 5 · 10 · Gradient of a line

  2. 2. Find the gradient of the line passing through (1, 8) and (4, 23).

    1 · 8 · 4 · 23 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 1) and (5, 13).

    1 · 1 · 5 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (5, 4) and (6, 6).

    5 · 4 · 6 · 6 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 9) and (7, 44).

    2 · 9 · 7 · 44 · Gradient of a line

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

    4 · 4 · 8 · 8 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 7) and (7, 27).

    3 · 7 · 7 · 27 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 4) and (11, 40).

    7 · 4 · 11 · 40 · Gradient of a line

  9. 9. Find the gradient of the line passing through (6, 7) and (11, 32).

    6 · 7 · 11 · 32 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 4) and (13, 46).

    7 · 4 · 13 · 46 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 10) and (11, 22).

    5 · 10 · 11 · 22 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 7) and (10, 19).

    4 · 7 · 10 · 19 · Gradient of a line
12 questions · Seed 42 · 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 (4, 8) and (5, 10).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 8) ÷ (5 − 4) = 2 ÷ 1 = 2.

  2. 2. Find the gradient of the line passing through (1, 8) and (4, 23).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 8) ÷ (4 − 1) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (1, 1) and (5, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (5 − 1) = 12 ÷ 4 = 3.

  4. 4. Find the gradient of the line passing through (5, 4) and (6, 6).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 4) ÷ (6 − 5) = 2 ÷ 1 = 2.

  5. 5. Find the gradient of the line passing through (2, 9) and (7, 44).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (44 − 9) ÷ (7 − 2) = 35 ÷ 5 = 7.

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

    1

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

  7. 7. Find the gradient of the line passing through (3, 7) and (7, 27).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 7) ÷ (7 − 3) = 20 ÷ 4 = 5.

  8. 8. Find the gradient of the line passing through (7, 4) and (11, 40).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (40 − 4) ÷ (11 − 7) = 36 ÷ 4 = 9.

  9. 9. Find the gradient of the line passing through (6, 7) and (11, 32).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (32 − 7) ÷ (11 − 6) = 25 ÷ 5 = 5.

  10. 10. Find the gradient of the line passing through (7, 4) and (13, 46).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 4) ÷ (13 − 7) = 42 ÷ 6 = 7.

  11. 11. Find the gradient of the line passing through (5, 10) and (11, 22).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 10) ÷ (11 − 5) = 12 ÷ 6 = 2.

  12. 12. Find the gradient of the line passing through (4, 7) and (10, 19).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (10 − 4) = 12 ÷ 6 = 2.

12 questions · Seed 42 · Age guidance, not curriculum certification