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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, 9) and (7, 27).

    4 · 9 · 7 · 27 · Gradient of a line

  2. 2. Find the gradient of the line passing through (8, 1) and (11, 28).

    8 · 1 · 11 · 28 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 3) and (12, 23).

    7 · 3 · 12 · 23 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (7, 29).

    4 · 5 · 7 · 29 · Gradient of a line

  5. 5. Find the gradient of the line passing through (6, 9) and (10, 13).

    6 · 9 · 10 · 13 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 9) and (10, 11).

    8 · 9 · 10 · 11 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 7) and (10, 19).

    6 · 7 · 10 · 19 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 1) and (9, 19).

    3 · 1 · 9 · 19 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 2) and (10, 6).

    8 · 2 · 10 · 6 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 4) and (11, 28).

    7 · 4 · 11 · 28 · Gradient of a line

  11. 11. Find the gradient of the line passing through (7, 9) and (13, 57).

    7 · 9 · 13 · 57 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 6) and (8, 46).

    3 · 6 · 8 · 46 · Gradient of a line
12 questions · Seed 104740 · 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, 9) and (7, 27).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 9) ÷ (7 − 4) = 18 ÷ 3 = 6.

  2. 2. Find the gradient of the line passing through (8, 1) and (11, 28).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 1) ÷ (11 − 8) = 27 ÷ 3 = 9.

  3. 3. Find the gradient of the line passing through (7, 3) and (12, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 3) ÷ (12 − 7) = 20 ÷ 5 = 4.

  4. 4. Find the gradient of the line passing through (4, 5) and (7, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (7 − 4) = 24 ÷ 3 = 8.

  5. 5. Find the gradient of the line passing through (6, 9) and (10, 13).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 9) ÷ (10 − 6) = 4 ÷ 4 = 1.

  6. 6. Find the gradient of the line passing through (8, 9) and (10, 11).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 9) ÷ (10 − 8) = 2 ÷ 2 = 1.

  7. 7. Find the gradient of the line passing through (6, 7) and (10, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (10 − 6) = 12 ÷ 4 = 3.

  8. 8. Find the gradient of the line passing through (3, 1) and (9, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 1) ÷ (9 − 3) = 18 ÷ 6 = 3.

  9. 9. Find the gradient of the line passing through (8, 2) and (10, 6).

    2

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

  10. 10. Find the gradient of the line passing through (7, 4) and (11, 28).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 4) ÷ (11 − 7) = 24 ÷ 4 = 6.

  11. 11. Find the gradient of the line passing through (7, 9) and (13, 57).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (57 − 9) ÷ (13 − 7) = 48 ÷ 6 = 8.

  12. 12. Find the gradient of the line passing through (3, 6) and (8, 46).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 6) ÷ (8 − 3) = 40 ÷ 5 = 8.

12 questions · Seed 104740 · 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, 9) and (7, 27).

    4 · 9 · 7 · 27 · Gradient of a line

  2. 2. Find the gradient of the line passing through (8, 1) and (11, 28).

    8 · 1 · 11 · 28 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 3) and (12, 23).

    7 · 3 · 12 · 23 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (7, 29).

    4 · 5 · 7 · 29 · Gradient of a line

  5. 5. Find the gradient of the line passing through (6, 9) and (10, 13).

    6 · 9 · 10 · 13 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 9) and (10, 11).

    8 · 9 · 10 · 11 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 7) and (10, 19).

    6 · 7 · 10 · 19 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 1) and (9, 19).

    3 · 1 · 9 · 19 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 2) and (10, 6).

    8 · 2 · 10 · 6 · Gradient of a line

  10. 10. Find the gradient of the line passing through (7, 4) and (11, 28).

    7 · 4 · 11 · 28 · Gradient of a line

  11. 11. Find the gradient of the line passing through (7, 9) and (13, 57).

    7 · 9 · 13 · 57 · Gradient of a line

  12. 12. Find the gradient of the line passing through (3, 6) and (8, 46).

    3 · 6 · 8 · 46 · Gradient of a line
12 questions · Seed 104740 · 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, 9) and (7, 27).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 9) ÷ (7 − 4) = 18 ÷ 3 = 6.

  2. 2. Find the gradient of the line passing through (8, 1) and (11, 28).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 1) ÷ (11 − 8) = 27 ÷ 3 = 9.

  3. 3. Find the gradient of the line passing through (7, 3) and (12, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 3) ÷ (12 − 7) = 20 ÷ 5 = 4.

  4. 4. Find the gradient of the line passing through (4, 5) and (7, 29).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (7 − 4) = 24 ÷ 3 = 8.

  5. 5. Find the gradient of the line passing through (6, 9) and (10, 13).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 9) ÷ (10 − 6) = 4 ÷ 4 = 1.

  6. 6. Find the gradient of the line passing through (8, 9) and (10, 11).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 9) ÷ (10 − 8) = 2 ÷ 2 = 1.

  7. 7. Find the gradient of the line passing through (6, 7) and (10, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (10 − 6) = 12 ÷ 4 = 3.

  8. 8. Find the gradient of the line passing through (3, 1) and (9, 19).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 1) ÷ (9 − 3) = 18 ÷ 6 = 3.

  9. 9. Find the gradient of the line passing through (8, 2) and (10, 6).

    2

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

  10. 10. Find the gradient of the line passing through (7, 4) and (11, 28).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 4) ÷ (11 − 7) = 24 ÷ 4 = 6.

  11. 11. Find the gradient of the line passing through (7, 9) and (13, 57).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (57 − 9) ÷ (13 − 7) = 48 ÷ 6 = 8.

  12. 12. Find the gradient of the line passing through (3, 6) and (8, 46).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 6) ÷ (8 − 3) = 40 ÷ 5 = 8.

12 questions · Seed 104740 · Age guidance, not curriculum certification