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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 (10, 52).

    5 · 7 · 10 · 52 · Gradient of a line

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

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

  3. 3. Find the gradient of the line passing through (8, 6) and (9, 15).

    8 · 6 · 9 · 15 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 7) and (7, 19).

    1 · 7 · 7 · 19 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 7) and (2, 15).

    1 · 7 · 2 · 15 · Gradient of a line

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

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

  7. 7. Find the gradient of the line passing through (2, 7) and (3, 10).

    2 · 7 · 3 · 10 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 3) and (13, 51).

    7 · 3 · 13 · 51 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 9) and (13, 14).

    8 · 9 · 13 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 5) and (7, 10).

    6 · 5 · 7 · 10 · Gradient of a line

  11. 11. Find the gradient of the line passing through (8, 1) and (11, 16).

    8 · 1 · 11 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 7) and (6, 39).

    2 · 7 · 6 · 39 · Gradient of a line
12 questions · Seed 104730 · 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 (10, 52).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (52 − 7) ÷ (10 − 5) = 45 ÷ 5 = 9.

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

    2

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

  3. 3. Find the gradient of the line passing through (8, 6) and (9, 15).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 6) ÷ (9 − 8) = 9 ÷ 1 = 9.

  4. 4. Find the gradient of the line passing through (1, 7) and (7, 19).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (7 − 1) = 12 ÷ 6 = 2.

  5. 5. Find the gradient of the line passing through (1, 7) and (2, 15).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 7) ÷ (2 − 1) = 8 ÷ 1 = 8.

  6. 6. 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.

  7. 7. Find the gradient of the line passing through (2, 7) and (3, 10).

    3

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

  8. 8. Find the gradient of the line passing through (7, 3) and (13, 51).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (51 − 3) ÷ (13 − 7) = 48 ÷ 6 = 8.

  9. 9. Find the gradient of the line passing through (8, 9) and (13, 14).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (13 − 8) = 5 ÷ 5 = 1.

  10. 10. Find the gradient of the line passing through (6, 5) and (7, 10).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 5) ÷ (7 − 6) = 5 ÷ 1 = 5.

  11. 11. Find the gradient of the line passing through (8, 1) and (11, 16).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 1) ÷ (11 − 8) = 15 ÷ 3 = 5.

  12. 12. Find the gradient of the line passing through (2, 7) and (6, 39).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 7) ÷ (6 − 2) = 32 ÷ 4 = 8.

12 questions · Seed 104730 · 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 (10, 52).

    5 · 7 · 10 · 52 · Gradient of a line

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

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

  3. 3. Find the gradient of the line passing through (8, 6) and (9, 15).

    8 · 6 · 9 · 15 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 7) and (7, 19).

    1 · 7 · 7 · 19 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 7) and (2, 15).

    1 · 7 · 2 · 15 · Gradient of a line

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

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

  7. 7. Find the gradient of the line passing through (2, 7) and (3, 10).

    2 · 7 · 3 · 10 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 3) and (13, 51).

    7 · 3 · 13 · 51 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 9) and (13, 14).

    8 · 9 · 13 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 5) and (7, 10).

    6 · 5 · 7 · 10 · Gradient of a line

  11. 11. Find the gradient of the line passing through (8, 1) and (11, 16).

    8 · 1 · 11 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 7) and (6, 39).

    2 · 7 · 6 · 39 · Gradient of a line
12 questions · Seed 104730 · 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 (10, 52).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (52 − 7) ÷ (10 − 5) = 45 ÷ 5 = 9.

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

    2

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

  3. 3. Find the gradient of the line passing through (8, 6) and (9, 15).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 6) ÷ (9 − 8) = 9 ÷ 1 = 9.

  4. 4. Find the gradient of the line passing through (1, 7) and (7, 19).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (7 − 1) = 12 ÷ 6 = 2.

  5. 5. Find the gradient of the line passing through (1, 7) and (2, 15).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 7) ÷ (2 − 1) = 8 ÷ 1 = 8.

  6. 6. 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.

  7. 7. Find the gradient of the line passing through (2, 7) and (3, 10).

    3

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

  8. 8. Find the gradient of the line passing through (7, 3) and (13, 51).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (51 − 3) ÷ (13 − 7) = 48 ÷ 6 = 8.

  9. 9. Find the gradient of the line passing through (8, 9) and (13, 14).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (13 − 8) = 5 ÷ 5 = 1.

  10. 10. Find the gradient of the line passing through (6, 5) and (7, 10).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 5) ÷ (7 − 6) = 5 ÷ 1 = 5.

  11. 11. Find the gradient of the line passing through (8, 1) and (11, 16).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 1) ÷ (11 − 8) = 15 ÷ 3 = 5.

  12. 12. Find the gradient of the line passing through (2, 7) and (6, 39).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 7) ÷ (6 − 2) = 32 ÷ 4 = 8.

12 questions · Seed 104730 · Age guidance, not curriculum certification