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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, 10) and (8, 26).

    4 · 10 · 8 · 26 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 7) and (12, 13).

    6 · 7 · 12 · 13 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 7) and (13, 22).

    8 · 7 · 13 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (8, 5) and (13, 20).

    8 · 5 · 13 · 20 · Gradient of a line

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

    5 · 5 · 8 · 20 · Gradient of a line

  6. 6. Find the gradient of the line passing through (6, 4) and (9, 13).

    6 · 4 · 9 · 13 · Gradient of a line

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

    2 · 5 · 8 · 17 · Gradient of a line

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

    6 · 5 · 9 · 11 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 3) and (7, 6).

    4 · 3 · 7 · 6 · Gradient of a line

  10. 10. Find the gradient of the line passing through (8, 5) and (14, 47).

    8 · 5 · 14 · 47 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 9) and (9, 21).

    5 · 9 · 9 · 21 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 10) and (5, 31).

    2 · 10 · 5 · 31 · Gradient of a line
12 questions · Seed 104749 · 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, 10) and (8, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 10) ÷ (8 − 4) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (6, 7) and (12, 13).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 7) ÷ (12 − 6) = 6 ÷ 6 = 1.

  3. 3. Find the gradient of the line passing through (8, 7) and (13, 22).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 7) ÷ (13 − 8) = 15 ÷ 5 = 3.

  4. 4. Find the gradient of the line passing through (8, 5) and (13, 20).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (13 − 8) = 15 ÷ 5 = 3.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (8 − 5) = 15 ÷ 3 = 5.

  6. 6. Find the gradient of the line passing through (6, 4) and (9, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 4) ÷ (9 − 6) = 9 ÷ 3 = 3.

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

    2

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

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (9 − 6) = 6 ÷ 3 = 2.

  9. 9. Find the gradient of the line passing through (4, 3) and (7, 6).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 3) ÷ (7 − 4) = 3 ÷ 3 = 1.

  10. 10. Find the gradient of the line passing through (8, 5) and (14, 47).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (47 − 5) ÷ (14 − 8) = 42 ÷ 6 = 7.

  11. 11. Find the gradient of the line passing through (5, 9) and (9, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (9 − 5) = 12 ÷ 4 = 3.

  12. 12. Find the gradient of the line passing through (2, 10) and (5, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 10) ÷ (5 − 2) = 21 ÷ 3 = 7.

12 questions · Seed 104749 · 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, 10) and (8, 26).

    4 · 10 · 8 · 26 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 7) and (12, 13).

    6 · 7 · 12 · 13 · Gradient of a line

  3. 3. Find the gradient of the line passing through (8, 7) and (13, 22).

    8 · 7 · 13 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (8, 5) and (13, 20).

    8 · 5 · 13 · 20 · Gradient of a line

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

    5 · 5 · 8 · 20 · Gradient of a line

  6. 6. Find the gradient of the line passing through (6, 4) and (9, 13).

    6 · 4 · 9 · 13 · Gradient of a line

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

    2 · 5 · 8 · 17 · Gradient of a line

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

    6 · 5 · 9 · 11 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 3) and (7, 6).

    4 · 3 · 7 · 6 · Gradient of a line

  10. 10. Find the gradient of the line passing through (8, 5) and (14, 47).

    8 · 5 · 14 · 47 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 9) and (9, 21).

    5 · 9 · 9 · 21 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 10) and (5, 31).

    2 · 10 · 5 · 31 · Gradient of a line
12 questions · Seed 104749 · 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, 10) and (8, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 10) ÷ (8 − 4) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (6, 7) and (12, 13).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 7) ÷ (12 − 6) = 6 ÷ 6 = 1.

  3. 3. Find the gradient of the line passing through (8, 7) and (13, 22).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 7) ÷ (13 − 8) = 15 ÷ 5 = 3.

  4. 4. Find the gradient of the line passing through (8, 5) and (13, 20).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (13 − 8) = 15 ÷ 5 = 3.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 5) ÷ (8 − 5) = 15 ÷ 3 = 5.

  6. 6. Find the gradient of the line passing through (6, 4) and (9, 13).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 4) ÷ (9 − 6) = 9 ÷ 3 = 3.

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

    2

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

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 5) ÷ (9 − 6) = 6 ÷ 3 = 2.

  9. 9. Find the gradient of the line passing through (4, 3) and (7, 6).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (6 − 3) ÷ (7 − 4) = 3 ÷ 3 = 1.

  10. 10. Find the gradient of the line passing through (8, 5) and (14, 47).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (47 − 5) ÷ (14 − 8) = 42 ÷ 6 = 7.

  11. 11. Find the gradient of the line passing through (5, 9) and (9, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (9 − 5) = 12 ÷ 4 = 3.

  12. 12. Find the gradient of the line passing through (2, 10) and (5, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 10) ÷ (5 − 2) = 21 ÷ 3 = 7.

12 questions · Seed 104749 · Age guidance, not curriculum certification