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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 (6, 9) and (9, 24).

    6 · 9 · 9 · 24 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 1) and (11, 25).

    5 · 1 · 11 · 25 · Gradient of a line

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

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

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

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

  5. 5. Find the gradient of the line passing through (2, 7) and (3, 12).

    2 · 7 · 3 · 12 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 1) and (2, 10).

    1 · 1 · 2 · 10 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 2) and (10, 5).

    7 · 2 · 10 · 5 · Gradient of a line

  8. 8. Find the gradient of the line passing through (4, 9) and (9, 44).

    4 · 9 · 9 · 44 · Gradient of a line

  9. 9. Find the gradient of the line passing through (1, 2) and (4, 14).

    1 · 2 · 4 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 10).

    6 · 2 · 10 · 10 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 3) and (6, 8).

    5 · 3 · 6 · 8 · Gradient of a line

  12. 12. Find the gradient of the line passing through (7, 10) and (11, 26).

    7 · 10 · 11 · 26 · Gradient of a line
12 questions · Seed 104742 · 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 (6, 9) and (9, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 9) ÷ (9 − 6) = 15 ÷ 3 = 5.

  2. 2. Find the gradient of the line passing through (5, 1) and (11, 25).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 1) ÷ (11 − 5) = 24 ÷ 6 = 4.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 5) ÷ (5 − 4) = 5 ÷ 1 = 5.

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

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (7 − 4) = 18 ÷ 3 = 6.

  5. 5. Find the gradient of the line passing through (2, 7) and (3, 12).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 7) ÷ (3 − 2) = 5 ÷ 1 = 5.

  6. 6. Find the gradient of the line passing through (1, 1) and (2, 10).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 1) ÷ (2 − 1) = 9 ÷ 1 = 9.

  7. 7. Find the gradient of the line passing through (7, 2) and (10, 5).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 2) ÷ (10 − 7) = 3 ÷ 3 = 1.

  8. 8. Find the gradient of the line passing through (4, 9) and (9, 44).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (44 − 9) ÷ (9 − 4) = 35 ÷ 5 = 7.

  9. 9. Find the gradient of the line passing through (1, 2) and (4, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 2) ÷ (4 − 1) = 12 ÷ 3 = 4.

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 10).

    2

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

  11. 11. Find the gradient of the line passing through (5, 3) and (6, 8).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 3) ÷ (6 − 5) = 5 ÷ 1 = 5.

  12. 12. Find the gradient of the line passing through (7, 10) and (11, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 10) ÷ (11 − 7) = 16 ÷ 4 = 4.

12 questions · Seed 104742 · 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 (6, 9) and (9, 24).

    6 · 9 · 9 · 24 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 1) and (11, 25).

    5 · 1 · 11 · 25 · Gradient of a line

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

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

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

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

  5. 5. Find the gradient of the line passing through (2, 7) and (3, 12).

    2 · 7 · 3 · 12 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 1) and (2, 10).

    1 · 1 · 2 · 10 · Gradient of a line

  7. 7. Find the gradient of the line passing through (7, 2) and (10, 5).

    7 · 2 · 10 · 5 · Gradient of a line

  8. 8. Find the gradient of the line passing through (4, 9) and (9, 44).

    4 · 9 · 9 · 44 · Gradient of a line

  9. 9. Find the gradient of the line passing through (1, 2) and (4, 14).

    1 · 2 · 4 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 10).

    6 · 2 · 10 · 10 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 3) and (6, 8).

    5 · 3 · 6 · 8 · Gradient of a line

  12. 12. Find the gradient of the line passing through (7, 10) and (11, 26).

    7 · 10 · 11 · 26 · Gradient of a line
12 questions · Seed 104742 · 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 (6, 9) and (9, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 9) ÷ (9 − 6) = 15 ÷ 3 = 5.

  2. 2. Find the gradient of the line passing through (5, 1) and (11, 25).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 1) ÷ (11 − 5) = 24 ÷ 6 = 4.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 5) ÷ (5 − 4) = 5 ÷ 1 = 5.

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

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (7 − 4) = 18 ÷ 3 = 6.

  5. 5. Find the gradient of the line passing through (2, 7) and (3, 12).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 7) ÷ (3 − 2) = 5 ÷ 1 = 5.

  6. 6. Find the gradient of the line passing through (1, 1) and (2, 10).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 1) ÷ (2 − 1) = 9 ÷ 1 = 9.

  7. 7. Find the gradient of the line passing through (7, 2) and (10, 5).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (5 − 2) ÷ (10 − 7) = 3 ÷ 3 = 1.

  8. 8. Find the gradient of the line passing through (4, 9) and (9, 44).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (44 − 9) ÷ (9 − 4) = 35 ÷ 5 = 7.

  9. 9. Find the gradient of the line passing through (1, 2) and (4, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 2) ÷ (4 − 1) = 12 ÷ 3 = 4.

  10. 10. Find the gradient of the line passing through (6, 2) and (10, 10).

    2

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

  11. 11. Find the gradient of the line passing through (5, 3) and (6, 8).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 3) ÷ (6 − 5) = 5 ÷ 1 = 5.

  12. 12. Find the gradient of the line passing through (7, 10) and (11, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 10) ÷ (11 − 7) = 16 ÷ 4 = 4.

12 questions · Seed 104742 · Age guidance, not curriculum certification