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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 (5, 7) and (8, 19).

    5 · 7 · 8 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 4) and (10, 29).

    5 · 4 · 10 · 29 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 7) and (4, 25).

    2 · 7 · 4 · 25 · Gradient of a line

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

    7 · 4 · 8 · 8 · Gradient of a line

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

    4 · 4 · 8 · 40 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 4) and (9, 19).

    4 · 4 · 9 · 19 · Gradient of a line

  7. 7. Find the gradient of the line passing through (1, 9) and (4, 15).

    1 · 9 · 4 · 15 · Gradient of a line

  8. 8. Find the gradient of the line passing through (8, 10) and (12, 30).

    8 · 10 · 12 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (2, 4) and (8, 58).

    2 · 4 · 8 · 58 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 9) and (10, 30).

    7 · 9 · 10 · 30 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 23).

    2 · 5 · 8 · 23 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 6) and (7, 34).

    3 · 6 · 7 · 34 · Gradient of a line
12 questions · Seed 104750 · 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 (5, 7) and (8, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (8 − 5) = 12 ÷ 3 = 4.

  2. 2. Find the gradient of the line passing through (5, 4) and (10, 29).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 4) ÷ (10 − 5) = 25 ÷ 5 = 5.

  3. 3. Find the gradient of the line passing through (2, 7) and (4, 25).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (4 − 2) = 18 ÷ 2 = 9.

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

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 4) ÷ (8 − 7) = 4 ÷ 1 = 4.

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

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (40 − 4) ÷ (8 − 4) = 36 ÷ 4 = 9.

  6. 6. Find the gradient of the line passing through (4, 4) and (9, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (9 − 4) = 15 ÷ 5 = 3.

  7. 7. Find the gradient of the line passing through (1, 9) and (4, 15).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 9) ÷ (4 − 1) = 6 ÷ 3 = 2.

  8. 8. Find the gradient of the line passing through (8, 10) and (12, 30).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (12 − 8) = 20 ÷ 4 = 5.

  9. 9. Find the gradient of the line passing through (2, 4) and (8, 58).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (58 − 4) ÷ (8 − 2) = 54 ÷ 6 = 9.

  10. 10. Find the gradient of the line passing through (7, 9) and (10, 30).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 9) ÷ (10 − 7) = 21 ÷ 3 = 7.

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 23).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 5) ÷ (8 − 2) = 18 ÷ 6 = 3.

  12. 12. Find the gradient of the line passing through (3, 6) and (7, 34).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 6) ÷ (7 − 3) = 28 ÷ 4 = 7.

12 questions · Seed 104750 · 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 (5, 7) and (8, 19).

    5 · 7 · 8 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 4) and (10, 29).

    5 · 4 · 10 · 29 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 7) and (4, 25).

    2 · 7 · 4 · 25 · Gradient of a line

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

    7 · 4 · 8 · 8 · Gradient of a line

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

    4 · 4 · 8 · 40 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 4) and (9, 19).

    4 · 4 · 9 · 19 · Gradient of a line

  7. 7. Find the gradient of the line passing through (1, 9) and (4, 15).

    1 · 9 · 4 · 15 · Gradient of a line

  8. 8. Find the gradient of the line passing through (8, 10) and (12, 30).

    8 · 10 · 12 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (2, 4) and (8, 58).

    2 · 4 · 8 · 58 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 9) and (10, 30).

    7 · 9 · 10 · 30 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 23).

    2 · 5 · 8 · 23 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 6) and (7, 34).

    3 · 6 · 7 · 34 · Gradient of a line
12 questions · Seed 104750 · 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 (5, 7) and (8, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (8 − 5) = 12 ÷ 3 = 4.

  2. 2. Find the gradient of the line passing through (5, 4) and (10, 29).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 4) ÷ (10 − 5) = 25 ÷ 5 = 5.

  3. 3. Find the gradient of the line passing through (2, 7) and (4, 25).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (4 − 2) = 18 ÷ 2 = 9.

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

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 4) ÷ (8 − 7) = 4 ÷ 1 = 4.

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

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (40 − 4) ÷ (8 − 4) = 36 ÷ 4 = 9.

  6. 6. Find the gradient of the line passing through (4, 4) and (9, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (9 − 4) = 15 ÷ 5 = 3.

  7. 7. Find the gradient of the line passing through (1, 9) and (4, 15).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 9) ÷ (4 − 1) = 6 ÷ 3 = 2.

  8. 8. Find the gradient of the line passing through (8, 10) and (12, 30).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 10) ÷ (12 − 8) = 20 ÷ 4 = 5.

  9. 9. Find the gradient of the line passing through (2, 4) and (8, 58).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (58 − 4) ÷ (8 − 2) = 54 ÷ 6 = 9.

  10. 10. Find the gradient of the line passing through (7, 9) and (10, 30).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 9) ÷ (10 − 7) = 21 ÷ 3 = 7.

  11. 11. Find the gradient of the line passing through (2, 5) and (8, 23).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 5) ÷ (8 − 2) = 18 ÷ 6 = 3.

  12. 12. Find the gradient of the line passing through (3, 6) and (7, 34).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 6) ÷ (7 − 3) = 28 ÷ 4 = 7.

12 questions · Seed 104750 · Age guidance, not curriculum certification