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MathsAges 13-15

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 13-15

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (7, 9) and (10, 36).

    7 · 9 · 10 · 36 · Gradient of a line

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

    5 · 5 · 8 · 11 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 2) and (3, 10).

    2 · 2 · 3 · 10 · Gradient of a line

  4. 4. Find the gradient of the line passing through (7, 1) and (9, 13).

    7 · 1 · 9 · 13 · Gradient of a line

  5. 5. Find the gradient of the line passing through (3, 3) and (4, 8).

    3 · 3 · 4 · 8 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 10) and (9, 30).

    4 · 10 · 9 · 30 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 9) and (4, 17).

    3 · 9 · 4 · 17 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 7) and (7, 61).

    1 · 7 · 7 · 61 · Gradient of a line

  9. 9. Find the gradient of the line passing through (2, 1) and (3, 2).

    2 · 1 · 3 · 2 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 4) and (8, 36).

    4 · 4 · 8 · 36 · Gradient of a line

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

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

  12. 12. Find the gradient of the line passing through (6, 6) and (8, 24).

    6 · 6 · 8 · 24 · Gradient of a line
12 questions · Seed 44 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (7, 9) and (10, 36).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 9) ÷ (10 − 7) = 27 ÷ 3 = 9.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (8 − 5) = 6 ÷ 3 = 2.

  3. 3. Find the gradient of the line passing through (2, 2) and (3, 10).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 2) ÷ (3 − 2) = 8 ÷ 1 = 8.

  4. 4. Find the gradient of the line passing through (7, 1) and (9, 13).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (9 − 7) = 12 ÷ 2 = 6.

  5. 5. Find the gradient of the line passing through (3, 3) and (4, 8).

    5

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

  6. 6. Find the gradient of the line passing through (4, 10) and (9, 30).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (9 − 4) = 20 ÷ 5 = 4.

  7. 7. Find the gradient of the line passing through (3, 9) and (4, 17).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 9) ÷ (4 − 3) = 8 ÷ 1 = 8.

  8. 8. Find the gradient of the line passing through (1, 7) and (7, 61).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (61 − 7) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (2, 1) and (3, 2).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (2 − 1) ÷ (3 − 2) = 1 ÷ 1 = 1.

  10. 10. Find the gradient of the line passing through (4, 4) and (8, 36).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 4) ÷ (8 − 4) = 32 ÷ 4 = 8.

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

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 7) ÷ (10 − 7) = 3 ÷ 3 = 1.

  12. 12. Find the gradient of the line passing through (6, 6) and (8, 24).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 6) ÷ (8 − 6) = 18 ÷ 2 = 9.

12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (7, 9) and (10, 36).

    7 · 9 · 10 · 36 · Gradient of a line

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

    5 · 5 · 8 · 11 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 2) and (3, 10).

    2 · 2 · 3 · 10 · Gradient of a line

  4. 4. Find the gradient of the line passing through (7, 1) and (9, 13).

    7 · 1 · 9 · 13 · Gradient of a line

  5. 5. Find the gradient of the line passing through (3, 3) and (4, 8).

    3 · 3 · 4 · 8 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 10) and (9, 30).

    4 · 10 · 9 · 30 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 9) and (4, 17).

    3 · 9 · 4 · 17 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 7) and (7, 61).

    1 · 7 · 7 · 61 · Gradient of a line

  9. 9. Find the gradient of the line passing through (2, 1) and (3, 2).

    2 · 1 · 3 · 2 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 4) and (8, 36).

    4 · 4 · 8 · 36 · Gradient of a line

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

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

  12. 12. Find the gradient of the line passing through (6, 6) and (8, 24).

    6 · 6 · 8 · 24 · Gradient of a line
12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (7, 9) and (10, 36).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 9) ÷ (10 − 7) = 27 ÷ 3 = 9.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (8 − 5) = 6 ÷ 3 = 2.

  3. 3. Find the gradient of the line passing through (2, 2) and (3, 10).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 2) ÷ (3 − 2) = 8 ÷ 1 = 8.

  4. 4. Find the gradient of the line passing through (7, 1) and (9, 13).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (9 − 7) = 12 ÷ 2 = 6.

  5. 5. Find the gradient of the line passing through (3, 3) and (4, 8).

    5

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

  6. 6. Find the gradient of the line passing through (4, 10) and (9, 30).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (9 − 4) = 20 ÷ 5 = 4.

  7. 7. Find the gradient of the line passing through (3, 9) and (4, 17).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 9) ÷ (4 − 3) = 8 ÷ 1 = 8.

  8. 8. Find the gradient of the line passing through (1, 7) and (7, 61).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (61 − 7) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (2, 1) and (3, 2).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (2 − 1) ÷ (3 − 2) = 1 ÷ 1 = 1.

  10. 10. Find the gradient of the line passing through (4, 4) and (8, 36).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 4) ÷ (8 − 4) = 32 ÷ 4 = 8.

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

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 7) ÷ (10 − 7) = 3 ÷ 3 = 1.

  12. 12. Find the gradient of the line passing through (6, 6) and (8, 24).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 6) ÷ (8 − 6) = 18 ÷ 2 = 9.

12 questions · Seed 44 · Age guidance, not curriculum certification