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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, 3) and (8, 31).

    4 · 3 · 8 · 31 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 6) and (9, 41).

    4 · 6 · 9 · 41 · Gradient of a line

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

    4 · 10 · 7 · 28 · Gradient of a line

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

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

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 36).

    5 · 1 · 10 · 36 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (6, 4).

    3 · 1 · 6 · 4 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 8) and (8, 16).

    6 · 8 · 8 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (8, 4) and (12, 24).

    8 · 4 · 12 · 24 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 8) and (14, 38).

    8 · 8 · 14 · 38 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 7) and (9, 52).

    4 · 7 · 9 · 52 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 4) and (8, 28).

    2 · 4 · 8 · 28 · Gradient of a line

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

    5 · 9 · 6 · 11 · Gradient of a line
12 questions · Seed 104748 · 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, 3) and (8, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 3) ÷ (8 − 4) = 28 ÷ 4 = 7.

  2. 2. Find the gradient of the line passing through (4, 6) and (9, 41).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (41 − 6) ÷ (9 − 4) = 35 ÷ 5 = 7.

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

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 10) ÷ (7 − 4) = 18 ÷ 3 = 6.

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

    1

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

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 36).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 1) ÷ (10 − 5) = 35 ÷ 5 = 7.

  6. 6. Find the gradient of the line passing through (3, 1) and (6, 4).

    1

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

  7. 7. Find the gradient of the line passing through (6, 8) and (8, 16).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 8) ÷ (8 − 6) = 8 ÷ 2 = 4.

  8. 8. Find the gradient of the line passing through (8, 4) and (12, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 4) ÷ (12 − 8) = 20 ÷ 4 = 5.

  9. 9. Find the gradient of the line passing through (8, 8) and (14, 38).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 8) ÷ (14 − 8) = 30 ÷ 6 = 5.

  10. 10. Find the gradient of the line passing through (4, 7) and (9, 52).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (52 − 7) ÷ (9 − 4) = 45 ÷ 5 = 9.

  11. 11. Find the gradient of the line passing through (2, 4) and (8, 28).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 4) ÷ (8 − 2) = 24 ÷ 6 = 4.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 9) ÷ (6 − 5) = 2 ÷ 1 = 2.

12 questions · Seed 104748 · 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, 3) and (8, 31).

    4 · 3 · 8 · 31 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 6) and (9, 41).

    4 · 6 · 9 · 41 · Gradient of a line

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

    4 · 10 · 7 · 28 · Gradient of a line

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

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

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 36).

    5 · 1 · 10 · 36 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (6, 4).

    3 · 1 · 6 · 4 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 8) and (8, 16).

    6 · 8 · 8 · 16 · Gradient of a line

  8. 8. Find the gradient of the line passing through (8, 4) and (12, 24).

    8 · 4 · 12 · 24 · Gradient of a line

  9. 9. Find the gradient of the line passing through (8, 8) and (14, 38).

    8 · 8 · 14 · 38 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 7) and (9, 52).

    4 · 7 · 9 · 52 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 4) and (8, 28).

    2 · 4 · 8 · 28 · Gradient of a line

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

    5 · 9 · 6 · 11 · Gradient of a line
12 questions · Seed 104748 · 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, 3) and (8, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 3) ÷ (8 − 4) = 28 ÷ 4 = 7.

  2. 2. Find the gradient of the line passing through (4, 6) and (9, 41).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (41 − 6) ÷ (9 − 4) = 35 ÷ 5 = 7.

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

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 10) ÷ (7 − 4) = 18 ÷ 3 = 6.

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

    1

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

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 36).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 1) ÷ (10 − 5) = 35 ÷ 5 = 7.

  6. 6. Find the gradient of the line passing through (3, 1) and (6, 4).

    1

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

  7. 7. Find the gradient of the line passing through (6, 8) and (8, 16).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 8) ÷ (8 − 6) = 8 ÷ 2 = 4.

  8. 8. Find the gradient of the line passing through (8, 4) and (12, 24).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (24 − 4) ÷ (12 − 8) = 20 ÷ 4 = 5.

  9. 9. Find the gradient of the line passing through (8, 8) and (14, 38).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (38 − 8) ÷ (14 − 8) = 30 ÷ 6 = 5.

  10. 10. Find the gradient of the line passing through (4, 7) and (9, 52).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (52 − 7) ÷ (9 − 4) = 45 ÷ 5 = 9.

  11. 11. Find the gradient of the line passing through (2, 4) and (8, 28).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (28 − 4) ÷ (8 − 2) = 24 ÷ 6 = 4.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 9) ÷ (6 − 5) = 2 ÷ 1 = 2.

12 questions · Seed 104748 · Age guidance, not curriculum certification