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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 (2, 10) and (7, 55).

    2 · 10 · 7 · 55 · Gradient of a line

  2. 2. Find the gradient of the line passing through (3, 3) and (6, 27).

    3 · 3 · 6 · 27 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 10) and (8, 30).

    4 · 10 · 8 · 30 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 3) and (8, 9).

    2 · 3 · 8 · 9 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 6) and (6, 14).

    4 · 6 · 6 · 14 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 5) and (7, 29).

    1 · 5 · 7 · 29 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 1) and (13, 55).

    7 · 1 · 13 · 55 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 4) and (6, 19).

    3 · 4 · 6 · 19 · Gradient of a line

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

    7 · 6 · 9 · 10 · Gradient of a line

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

    1 · 1 · 3 · 5 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 2) and (6, 5).

    5 · 2 · 6 · 5 · Gradient of a line

  12. 12. Find the gradient of the line passing through (5, 3) and (11, 57).

    5 · 3 · 11 · 57 · Gradient of a line
12 questions · Seed 104741 · 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 (2, 10) and (7, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 10) ÷ (7 − 2) = 45 ÷ 5 = 9.

  2. 2. Find the gradient of the line passing through (3, 3) and (6, 27).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 3) ÷ (6 − 3) = 24 ÷ 3 = 8.

  3. 3. Find the gradient of the line passing through (4, 10) and (8, 30).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (8 − 4) = 20 ÷ 4 = 5.

  4. 4. Find the gradient of the line passing through (2, 3) and (8, 9).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 3) ÷ (8 − 2) = 6 ÷ 6 = 1.

  5. 5. Find the gradient of the line passing through (4, 6) and (6, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 6) ÷ (6 − 4) = 8 ÷ 2 = 4.

  6. 6. Find the gradient of the line passing through (1, 5) and (7, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (7 − 1) = 24 ÷ 6 = 4.

  7. 7. Find the gradient of the line passing through (7, 1) and (13, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 1) ÷ (13 − 7) = 54 ÷ 6 = 9.

  8. 8. Find the gradient of the line passing through (3, 4) and (6, 19).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (6 − 3) = 15 ÷ 3 = 5.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 6) ÷ (9 − 7) = 4 ÷ 2 = 2.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 1) ÷ (3 − 1) = 4 ÷ 2 = 2.

  11. 11. Find the gradient of the line passing through (5, 2) and (6, 5).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 2) ÷ (6 − 5) = 3 ÷ 1 = 3.

  12. 12. Find the gradient of the line passing through (5, 3) and (11, 57).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (57 − 3) ÷ (11 − 5) = 54 ÷ 6 = 9.

12 questions · Seed 104741 · 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 (2, 10) and (7, 55).

    2 · 10 · 7 · 55 · Gradient of a line

  2. 2. Find the gradient of the line passing through (3, 3) and (6, 27).

    3 · 3 · 6 · 27 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 10) and (8, 30).

    4 · 10 · 8 · 30 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 3) and (8, 9).

    2 · 3 · 8 · 9 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 6) and (6, 14).

    4 · 6 · 6 · 14 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 5) and (7, 29).

    1 · 5 · 7 · 29 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 1) and (13, 55).

    7 · 1 · 13 · 55 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 4) and (6, 19).

    3 · 4 · 6 · 19 · Gradient of a line

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

    7 · 6 · 9 · 10 · Gradient of a line

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

    1 · 1 · 3 · 5 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 2) and (6, 5).

    5 · 2 · 6 · 5 · Gradient of a line

  12. 12. Find the gradient of the line passing through (5, 3) and (11, 57).

    5 · 3 · 11 · 57 · Gradient of a line
12 questions · Seed 104741 · 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 (2, 10) and (7, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 10) ÷ (7 − 2) = 45 ÷ 5 = 9.

  2. 2. Find the gradient of the line passing through (3, 3) and (6, 27).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 3) ÷ (6 − 3) = 24 ÷ 3 = 8.

  3. 3. Find the gradient of the line passing through (4, 10) and (8, 30).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (8 − 4) = 20 ÷ 4 = 5.

  4. 4. Find the gradient of the line passing through (2, 3) and (8, 9).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 3) ÷ (8 − 2) = 6 ÷ 6 = 1.

  5. 5. Find the gradient of the line passing through (4, 6) and (6, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 6) ÷ (6 − 4) = 8 ÷ 2 = 4.

  6. 6. Find the gradient of the line passing through (1, 5) and (7, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (7 − 1) = 24 ÷ 6 = 4.

  7. 7. Find the gradient of the line passing through (7, 1) and (13, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 1) ÷ (13 − 7) = 54 ÷ 6 = 9.

  8. 8. Find the gradient of the line passing through (3, 4) and (6, 19).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (6 − 3) = 15 ÷ 3 = 5.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 6) ÷ (9 − 7) = 4 ÷ 2 = 2.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 1) ÷ (3 − 1) = 4 ÷ 2 = 2.

  11. 11. Find the gradient of the line passing through (5, 2) and (6, 5).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 2) ÷ (6 − 5) = 3 ÷ 1 = 3.

  12. 12. Find the gradient of the line passing through (5, 3) and (11, 57).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (57 − 3) ÷ (11 − 5) = 54 ÷ 6 = 9.

12 questions · Seed 104741 · Age guidance, not curriculum certification