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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, 10) and (6, 18).

    4 · 10 · 6 · 18 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 1) and (6, 7).

    4 · 1 · 6 · 7 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 4) and (11, 25).

    8 · 4 · 11 · 25 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 8) and (8, 14).

    6 · 8 · 8 · 14 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 2) and (3, 8).

    1 · 2 · 3 · 8 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 5) and (6, 29).

    3 · 5 · 6 · 29 · Gradient of a line

  7. 7. Find the gradient of the line passing through (1, 5) and (3, 11).

    1 · 5 · 3 · 11 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (7, 60).

    1 · 6 · 7 · 60 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 6) and (5, 22).

    3 · 6 · 5 · 22 · Gradient of a line

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

    8 · 6 · 9 · 7 · Gradient of a line

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 31).

    4 · 7 · 10 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 8) and (5, 26).

    3 · 8 · 5 · 26 · Gradient of a line
12 questions · Seed 104737 · 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, 10) and (6, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 10) ÷ (6 − 4) = 8 ÷ 2 = 4.

  2. 2. Find the gradient of the line passing through (4, 1) and (6, 7).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (6 − 4) = 6 ÷ 2 = 3.

  3. 3. Find the gradient of the line passing through (8, 4) and (11, 25).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 4) ÷ (11 − 8) = 21 ÷ 3 = 7.

  4. 4. Find the gradient of the line passing through (6, 8) and (8, 14).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 8) ÷ (8 − 6) = 6 ÷ 2 = 3.

  5. 5. Find the gradient of the line passing through (1, 2) and (3, 8).

    3

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

  6. 6. Find the gradient of the line passing through (3, 5) and (6, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (6 − 3) = 24 ÷ 3 = 8.

  7. 7. Find the gradient of the line passing through (1, 5) and (3, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (3 − 1) = 6 ÷ 2 = 3.

  8. 8. Find the gradient of the line passing through (1, 6) and (7, 60).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (60 − 6) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (3, 6) and (5, 22).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 6) ÷ (5 − 3) = 16 ÷ 2 = 8.

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

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 6) ÷ (9 − 8) = 1 ÷ 1 = 1.

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 31).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 7) ÷ (10 − 4) = 24 ÷ 6 = 4.

  12. 12. Find the gradient of the line passing through (3, 8) and (5, 26).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (5 − 3) = 18 ÷ 2 = 9.

12 questions · Seed 104737 · 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, 10) and (6, 18).

    4 · 10 · 6 · 18 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 1) and (6, 7).

    4 · 1 · 6 · 7 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 4) and (11, 25).

    8 · 4 · 11 · 25 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 8) and (8, 14).

    6 · 8 · 8 · 14 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 2) and (3, 8).

    1 · 2 · 3 · 8 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 5) and (6, 29).

    3 · 5 · 6 · 29 · Gradient of a line

  7. 7. Find the gradient of the line passing through (1, 5) and (3, 11).

    1 · 5 · 3 · 11 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (7, 60).

    1 · 6 · 7 · 60 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 6) and (5, 22).

    3 · 6 · 5 · 22 · Gradient of a line

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

    8 · 6 · 9 · 7 · Gradient of a line

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 31).

    4 · 7 · 10 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 8) and (5, 26).

    3 · 8 · 5 · 26 · Gradient of a line
12 questions · Seed 104737 · 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, 10) and (6, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 10) ÷ (6 − 4) = 8 ÷ 2 = 4.

  2. 2. Find the gradient of the line passing through (4, 1) and (6, 7).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (6 − 4) = 6 ÷ 2 = 3.

  3. 3. Find the gradient of the line passing through (8, 4) and (11, 25).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 4) ÷ (11 − 8) = 21 ÷ 3 = 7.

  4. 4. Find the gradient of the line passing through (6, 8) and (8, 14).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 8) ÷ (8 − 6) = 6 ÷ 2 = 3.

  5. 5. Find the gradient of the line passing through (1, 2) and (3, 8).

    3

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

  6. 6. Find the gradient of the line passing through (3, 5) and (6, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (6 − 3) = 24 ÷ 3 = 8.

  7. 7. Find the gradient of the line passing through (1, 5) and (3, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (3 − 1) = 6 ÷ 2 = 3.

  8. 8. Find the gradient of the line passing through (1, 6) and (7, 60).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (60 − 6) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (3, 6) and (5, 22).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 6) ÷ (5 − 3) = 16 ÷ 2 = 8.

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

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 6) ÷ (9 − 8) = 1 ÷ 1 = 1.

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 31).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 7) ÷ (10 − 4) = 24 ÷ 6 = 4.

  12. 12. Find the gradient of the line passing through (3, 8) and (5, 26).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (5 − 3) = 18 ÷ 2 = 9.

12 questions · Seed 104737 · Age guidance, not curriculum certification