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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 (7, 9) and (10, 30).

    7 · 9 · 10 · 30 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 10) and (7, 25).

    4 · 10 · 7 · 25 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 4) and (3, 12).

    2 · 4 · 3 · 12 · Gradient of a line

  4. 4. Find the gradient of the line passing through (5, 6) and (7, 8).

    5 · 6 · 7 · 8 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 6) and (13, 21).

    8 · 6 · 13 · 21 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 2) and (5, 14).

    2 · 2 · 5 · 14 · Gradient of a line

  7. 7. Find the gradient of the line passing through (2, 10) and (7, 15).

    2 · 10 · 7 · 15 · Gradient of a line

  8. 8. Find the gradient of the line passing through (6, 5) and (9, 14).

    6 · 5 · 9 · 14 · Gradient of a line

  9. 9. Find the gradient of the line passing through (7, 7) and (10, 22).

    7 · 7 · 10 · 22 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 10) and (9, 15).

    4 · 10 · 9 · 15 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 10) and (8, 31).

    5 · 10 · 8 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (5, 7) and (11, 37).

    5 · 7 · 11 · 37 · Gradient of a line
12 questions · Seed 104738 · 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 (7, 9) and (10, 30).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 9) ÷ (10 − 7) = 21 ÷ 3 = 7.

  2. 2. Find the gradient of the line passing through (4, 10) and (7, 25).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 10) ÷ (7 − 4) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (2, 4) and (3, 12).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 4) ÷ (3 − 2) = 8 ÷ 1 = 8.

  4. 4. Find the gradient of the line passing through (5, 6) and (7, 8).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 6) ÷ (7 − 5) = 2 ÷ 2 = 1.

  5. 5. Find the gradient of the line passing through (8, 6) and (13, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 6) ÷ (13 − 8) = 15 ÷ 5 = 3.

  6. 6. Find the gradient of the line passing through (2, 2) and (5, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 2) ÷ (5 − 2) = 12 ÷ 3 = 4.

  7. 7. Find the gradient of the line passing through (2, 10) and (7, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 10) ÷ (7 − 2) = 5 ÷ 5 = 1.

  8. 8. Find the gradient of the line passing through (6, 5) and (9, 14).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 5) ÷ (9 − 6) = 9 ÷ 3 = 3.

  9. 9. Find the gradient of the line passing through (7, 7) and (10, 22).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 7) ÷ (10 − 7) = 15 ÷ 3 = 5.

  10. 10. Find the gradient of the line passing through (4, 10) and (9, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 10) ÷ (9 − 4) = 5 ÷ 5 = 1.

  11. 11. Find the gradient of the line passing through (5, 10) and (8, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 10) ÷ (8 − 5) = 21 ÷ 3 = 7.

  12. 12. Find the gradient of the line passing through (5, 7) and (11, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (11 − 5) = 30 ÷ 6 = 5.

12 questions · Seed 104738 · 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 (7, 9) and (10, 30).

    7 · 9 · 10 · 30 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 10) and (7, 25).

    4 · 10 · 7 · 25 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 4) and (3, 12).

    2 · 4 · 3 · 12 · Gradient of a line

  4. 4. Find the gradient of the line passing through (5, 6) and (7, 8).

    5 · 6 · 7 · 8 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 6) and (13, 21).

    8 · 6 · 13 · 21 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 2) and (5, 14).

    2 · 2 · 5 · 14 · Gradient of a line

  7. 7. Find the gradient of the line passing through (2, 10) and (7, 15).

    2 · 10 · 7 · 15 · Gradient of a line

  8. 8. Find the gradient of the line passing through (6, 5) and (9, 14).

    6 · 5 · 9 · 14 · Gradient of a line

  9. 9. Find the gradient of the line passing through (7, 7) and (10, 22).

    7 · 7 · 10 · 22 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 10) and (9, 15).

    4 · 10 · 9 · 15 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 10) and (8, 31).

    5 · 10 · 8 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (5, 7) and (11, 37).

    5 · 7 · 11 · 37 · Gradient of a line
12 questions · Seed 104738 · 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 (7, 9) and (10, 30).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 9) ÷ (10 − 7) = 21 ÷ 3 = 7.

  2. 2. Find the gradient of the line passing through (4, 10) and (7, 25).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 10) ÷ (7 − 4) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (2, 4) and (3, 12).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 4) ÷ (3 − 2) = 8 ÷ 1 = 8.

  4. 4. Find the gradient of the line passing through (5, 6) and (7, 8).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 6) ÷ (7 − 5) = 2 ÷ 2 = 1.

  5. 5. Find the gradient of the line passing through (8, 6) and (13, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 6) ÷ (13 − 8) = 15 ÷ 5 = 3.

  6. 6. Find the gradient of the line passing through (2, 2) and (5, 14).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 2) ÷ (5 − 2) = 12 ÷ 3 = 4.

  7. 7. Find the gradient of the line passing through (2, 10) and (7, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 10) ÷ (7 − 2) = 5 ÷ 5 = 1.

  8. 8. Find the gradient of the line passing through (6, 5) and (9, 14).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 5) ÷ (9 − 6) = 9 ÷ 3 = 3.

  9. 9. Find the gradient of the line passing through (7, 7) and (10, 22).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 7) ÷ (10 − 7) = 15 ÷ 3 = 5.

  10. 10. Find the gradient of the line passing through (4, 10) and (9, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 10) ÷ (9 − 4) = 5 ÷ 5 = 1.

  11. 11. Find the gradient of the line passing through (5, 10) and (8, 31).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 10) ÷ (8 − 5) = 21 ÷ 3 = 7.

  12. 12. Find the gradient of the line passing through (5, 7) and (11, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (11 − 5) = 30 ÷ 6 = 5.

12 questions · Seed 104738 · Age guidance, not curriculum certification