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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, 4) and (6, 19).

    3 · 4 · 6 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 9) and (8, 23).

    6 · 9 · 8 · 23 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 3) and (5, 8).

    4 · 3 · 5 · 8 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 3) and (5, 24).

    2 · 3 · 5 · 24 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 5) and (6, 23).

    4 · 5 · 6 · 23 · Gradient of a line

  6. 6. Find the gradient of the line passing through (6, 3) and (11, 23).

    6 · 3 · 11 · 23 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 4) and (5, 16).

    3 · 4 · 5 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (6, 1) and (8, 13).

    6 · 1 · 8 · 13 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 10) and (4, 14).

    3 · 10 · 4 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (3, 1) and (4, 8).

    3 · 1 · 4 · 8 · Gradient of a line

  11. 11. Find the gradient of the line passing through (1, 4) and (3, 16).

    1 · 4 · 3 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 8) and (9, 18).

    4 · 8 · 9 · 18 · Gradient of a line
12 questions · Seed 104746 · 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, 4) and (6, 19).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (6 − 3) = 15 ÷ 3 = 5.

  2. 2. Find the gradient of the line passing through (6, 9) and (8, 23).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 9) ÷ (8 − 6) = 14 ÷ 2 = 7.

  3. 3. Find the gradient of the line passing through (4, 3) and (5, 8).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 3) ÷ (5 − 4) = 5 ÷ 1 = 5.

  4. 4. Find the gradient of the line passing through (2, 3) and (5, 24).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 3) ÷ (5 − 2) = 21 ÷ 3 = 7.

  5. 5. Find the gradient of the line passing through (4, 5) and (6, 23).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 5) ÷ (6 − 4) = 18 ÷ 2 = 9.

  6. 6. Find the gradient of the line passing through (6, 3) and (11, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 3) ÷ (11 − 6) = 20 ÷ 5 = 4.

  7. 7. Find the gradient of the line passing through (3, 4) and (5, 16).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 4) ÷ (5 − 3) = 12 ÷ 2 = 6.

  8. 8. Find the gradient of the line passing through (6, 1) and (8, 13).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (8 − 6) = 12 ÷ 2 = 6.

  9. 9. Find the gradient of the line passing through (3, 10) and (4, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 10) ÷ (4 − 3) = 4 ÷ 1 = 4.

  10. 10. Find the gradient of the line passing through (3, 1) and (4, 8).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 1) ÷ (4 − 3) = 7 ÷ 1 = 7.

  11. 11. Find the gradient of the line passing through (1, 4) and (3, 16).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 4) ÷ (3 − 1) = 12 ÷ 2 = 6.

  12. 12. Find the gradient of the line passing through (4, 8) and (9, 18).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 8) ÷ (9 − 4) = 10 ÷ 5 = 2.

12 questions · Seed 104746 · 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, 4) and (6, 19).

    3 · 4 · 6 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (6, 9) and (8, 23).

    6 · 9 · 8 · 23 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 3) and (5, 8).

    4 · 3 · 5 · 8 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 3) and (5, 24).

    2 · 3 · 5 · 24 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 5) and (6, 23).

    4 · 5 · 6 · 23 · Gradient of a line

  6. 6. Find the gradient of the line passing through (6, 3) and (11, 23).

    6 · 3 · 11 · 23 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 4) and (5, 16).

    3 · 4 · 5 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (6, 1) and (8, 13).

    6 · 1 · 8 · 13 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 10) and (4, 14).

    3 · 10 · 4 · 14 · Gradient of a line

  10. 10. Find the gradient of the line passing through (3, 1) and (4, 8).

    3 · 1 · 4 · 8 · Gradient of a line

  11. 11. Find the gradient of the line passing through (1, 4) and (3, 16).

    1 · 4 · 3 · 16 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 8) and (9, 18).

    4 · 8 · 9 · 18 · Gradient of a line
12 questions · Seed 104746 · 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, 4) and (6, 19).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 4) ÷ (6 − 3) = 15 ÷ 3 = 5.

  2. 2. Find the gradient of the line passing through (6, 9) and (8, 23).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 9) ÷ (8 − 6) = 14 ÷ 2 = 7.

  3. 3. Find the gradient of the line passing through (4, 3) and (5, 8).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 3) ÷ (5 − 4) = 5 ÷ 1 = 5.

  4. 4. Find the gradient of the line passing through (2, 3) and (5, 24).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 3) ÷ (5 − 2) = 21 ÷ 3 = 7.

  5. 5. Find the gradient of the line passing through (4, 5) and (6, 23).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 5) ÷ (6 − 4) = 18 ÷ 2 = 9.

  6. 6. Find the gradient of the line passing through (6, 3) and (11, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 3) ÷ (11 − 6) = 20 ÷ 5 = 4.

  7. 7. Find the gradient of the line passing through (3, 4) and (5, 16).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 4) ÷ (5 − 3) = 12 ÷ 2 = 6.

  8. 8. Find the gradient of the line passing through (6, 1) and (8, 13).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 1) ÷ (8 − 6) = 12 ÷ 2 = 6.

  9. 9. Find the gradient of the line passing through (3, 10) and (4, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 10) ÷ (4 − 3) = 4 ÷ 1 = 4.

  10. 10. Find the gradient of the line passing through (3, 1) and (4, 8).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 1) ÷ (4 − 3) = 7 ÷ 1 = 7.

  11. 11. Find the gradient of the line passing through (1, 4) and (3, 16).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 4) ÷ (3 − 1) = 12 ÷ 2 = 6.

  12. 12. Find the gradient of the line passing through (4, 8) and (9, 18).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 8) ÷ (9 − 4) = 10 ÷ 5 = 2.

12 questions · Seed 104746 · Age guidance, not curriculum certification