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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 (3, 5) and (7, 21).

    3 · 5 · 7 · 21 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 5) and (8, 17).

    6 · 5 · 8 · 17 · Gradient of a line

  3. 3. Find the gradient of the line passing through (6, 3) and (11, 48).

    6 · 3 · 11 · 48 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (6, 11).

    4 · 5 · 6 · 11 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 5) and (10, 11).

    8 · 5 · 10 · 11 · Gradient of a line

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

    7 · 1 · 9 · 15 · Gradient of a line

  7. 7. Find the gradient of the line passing through (4, 9) and (9, 29).

    4 · 9 · 9 · 29 · Gradient of a line

  8. 8. Find the gradient of the line passing through (4, 5) and (9, 20).

    4 · 5 · 9 · 20 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 8) and (9, 43).

    4 · 8 · 9 · 43 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 4) and (10, 24).

    6 · 4 · 10 · 24 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 9) and (6, 16).

    5 · 9 · 6 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (6, 8) and (10, 16).

    6 · 8 · 10 · 16 · Gradient of a line
12 questions · Seed 104733 · 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 (3, 5) and (7, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (7 − 3) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (6, 5) and (8, 17).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 5) ÷ (8 − 6) = 12 ÷ 2 = 6.

  3. 3. Find the gradient of the line passing through (6, 3) and (11, 48).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (48 − 3) ÷ (11 − 6) = 45 ÷ 5 = 9.

  4. 4. Find the gradient of the line passing through (4, 5) and (6, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (6 − 4) = 6 ÷ 2 = 3.

  5. 5. Find the gradient of the line passing through (8, 5) and (10, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (10 − 8) = 6 ÷ 2 = 3.

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

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 1) ÷ (9 − 7) = 14 ÷ 2 = 7.

  7. 7. Find the gradient of the line passing through (4, 9) and (9, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 9) ÷ (9 − 4) = 20 ÷ 5 = 4.

  8. 8. Find the gradient of the line passing through (4, 5) and (9, 20).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (9 − 4) = 15 ÷ 5 = 3.

  9. 9. Find the gradient of the line passing through (4, 8) and (9, 43).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (43 − 8) ÷ (9 − 4) = 35 ÷ 5 = 7.

  10. 10. Find the gradient of the line passing through (6, 4) and (10, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 4) ÷ (10 − 6) = 20 ÷ 4 = 5.

  11. 11. Find the gradient of the line passing through (5, 9) and (6, 16).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 9) ÷ (6 − 5) = 7 ÷ 1 = 7.

  12. 12. Find the gradient of the line passing through (6, 8) and (10, 16).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 8) ÷ (10 − 6) = 8 ÷ 4 = 2.

12 questions · Seed 104733 · 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 (3, 5) and (7, 21).

    3 · 5 · 7 · 21 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 5) and (8, 17).

    6 · 5 · 8 · 17 · Gradient of a line

  3. 3. Find the gradient of the line passing through (6, 3) and (11, 48).

    6 · 3 · 11 · 48 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (6, 11).

    4 · 5 · 6 · 11 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 5) and (10, 11).

    8 · 5 · 10 · 11 · Gradient of a line

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

    7 · 1 · 9 · 15 · Gradient of a line

  7. 7. Find the gradient of the line passing through (4, 9) and (9, 29).

    4 · 9 · 9 · 29 · Gradient of a line

  8. 8. Find the gradient of the line passing through (4, 5) and (9, 20).

    4 · 5 · 9 · 20 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 8) and (9, 43).

    4 · 8 · 9 · 43 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 4) and (10, 24).

    6 · 4 · 10 · 24 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 9) and (6, 16).

    5 · 9 · 6 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (6, 8) and (10, 16).

    6 · 8 · 10 · 16 · Gradient of a line
12 questions · Seed 104733 · 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 (3, 5) and (7, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (7 − 3) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (6, 5) and (8, 17).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 5) ÷ (8 − 6) = 12 ÷ 2 = 6.

  3. 3. Find the gradient of the line passing through (6, 3) and (11, 48).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (48 − 3) ÷ (11 − 6) = 45 ÷ 5 = 9.

  4. 4. Find the gradient of the line passing through (4, 5) and (6, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (6 − 4) = 6 ÷ 2 = 3.

  5. 5. Find the gradient of the line passing through (8, 5) and (10, 11).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (10 − 8) = 6 ÷ 2 = 3.

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

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 1) ÷ (9 − 7) = 14 ÷ 2 = 7.

  7. 7. Find the gradient of the line passing through (4, 9) and (9, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 9) ÷ (9 − 4) = 20 ÷ 5 = 4.

  8. 8. Find the gradient of the line passing through (4, 5) and (9, 20).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (9 − 4) = 15 ÷ 5 = 3.

  9. 9. Find the gradient of the line passing through (4, 8) and (9, 43).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (43 − 8) ÷ (9 − 4) = 35 ÷ 5 = 7.

  10. 10. Find the gradient of the line passing through (6, 4) and (10, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 4) ÷ (10 − 6) = 20 ÷ 4 = 5.

  11. 11. Find the gradient of the line passing through (5, 9) and (6, 16).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 9) ÷ (6 − 5) = 7 ÷ 1 = 7.

  12. 12. Find the gradient of the line passing through (6, 8) and (10, 16).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 8) ÷ (10 − 6) = 8 ÷ 4 = 2.

12 questions · Seed 104733 · Age guidance, not curriculum certification