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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, 7) and (10, 37).

    4 · 7 · 10 · 37 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (8, 12).

    5 · 9 · 8 · 12 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 2) and (6, 12).

    1 · 2 · 6 · 12 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 1) and (5, 37).

    1 · 1 · 5 · 37 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 1) and (3, 15).

    1 · 1 · 3 · 15 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 9) and (8, 45).

    2 · 9 · 8 · 45 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 9) and (12, 39).

    6 · 9 · 12 · 39 · Gradient of a line

  8. 8. Find the gradient of the line passing through (5, 4) and (9, 8).

    5 · 4 · 9 · 8 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 2) and (10, 26).

    4 · 2 · 10 · 26 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 1) and (8, 25).

    4 · 1 · 8 · 25 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 6) and (6, 34).

    2 · 6 · 6 · 34 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 9) and (3, 14).

    2 · 9 · 3 · 14 · Gradient of a line
12 questions · Seed 104744 · 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, 7) and (10, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (10 − 4) = 30 ÷ 6 = 5.

  2. 2. Find the gradient of the line passing through (5, 9) and (8, 12).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 9) ÷ (8 − 5) = 3 ÷ 3 = 1.

  3. 3. Find the gradient of the line passing through (1, 2) and (6, 12).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 2) ÷ (6 − 1) = 10 ÷ 5 = 2.

  4. 4. Find the gradient of the line passing through (1, 1) and (5, 37).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 1) ÷ (5 − 1) = 36 ÷ 4 = 9.

  5. 5. Find the gradient of the line passing through (1, 1) and (3, 15).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 1) ÷ (3 − 1) = 14 ÷ 2 = 7.

  6. 6. Find the gradient of the line passing through (2, 9) and (8, 45).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 9) ÷ (8 − 2) = 36 ÷ 6 = 6.

  7. 7. Find the gradient of the line passing through (6, 9) and (12, 39).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 9) ÷ (12 − 6) = 30 ÷ 6 = 5.

  8. 8. Find the gradient of the line passing through (5, 4) and (9, 8).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 4) ÷ (9 − 5) = 4 ÷ 4 = 1.

  9. 9. Find the gradient of the line passing through (4, 2) and (10, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 2) ÷ (10 − 4) = 24 ÷ 6 = 4.

  10. 10. Find the gradient of the line passing through (4, 1) and (8, 25).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 1) ÷ (8 − 4) = 24 ÷ 4 = 6.

  11. 11. Find the gradient of the line passing through (2, 6) and (6, 34).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 6) ÷ (6 − 2) = 28 ÷ 4 = 7.

  12. 12. Find the gradient of the line passing through (2, 9) and (3, 14).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (3 − 2) = 5 ÷ 1 = 5.

12 questions · Seed 104744 · 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, 7) and (10, 37).

    4 · 7 · 10 · 37 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (8, 12).

    5 · 9 · 8 · 12 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 2) and (6, 12).

    1 · 2 · 6 · 12 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 1) and (5, 37).

    1 · 1 · 5 · 37 · Gradient of a line

  5. 5. Find the gradient of the line passing through (1, 1) and (3, 15).

    1 · 1 · 3 · 15 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 9) and (8, 45).

    2 · 9 · 8 · 45 · Gradient of a line

  7. 7. Find the gradient of the line passing through (6, 9) and (12, 39).

    6 · 9 · 12 · 39 · Gradient of a line

  8. 8. Find the gradient of the line passing through (5, 4) and (9, 8).

    5 · 4 · 9 · 8 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 2) and (10, 26).

    4 · 2 · 10 · 26 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 1) and (8, 25).

    4 · 1 · 8 · 25 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 6) and (6, 34).

    2 · 6 · 6 · 34 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 9) and (3, 14).

    2 · 9 · 3 · 14 · Gradient of a line
12 questions · Seed 104744 · 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, 7) and (10, 37).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 7) ÷ (10 − 4) = 30 ÷ 6 = 5.

  2. 2. Find the gradient of the line passing through (5, 9) and (8, 12).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 9) ÷ (8 − 5) = 3 ÷ 3 = 1.

  3. 3. Find the gradient of the line passing through (1, 2) and (6, 12).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 2) ÷ (6 − 1) = 10 ÷ 5 = 2.

  4. 4. Find the gradient of the line passing through (1, 1) and (5, 37).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (37 − 1) ÷ (5 − 1) = 36 ÷ 4 = 9.

  5. 5. Find the gradient of the line passing through (1, 1) and (3, 15).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 1) ÷ (3 − 1) = 14 ÷ 2 = 7.

  6. 6. Find the gradient of the line passing through (2, 9) and (8, 45).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 9) ÷ (8 − 2) = 36 ÷ 6 = 6.

  7. 7. Find the gradient of the line passing through (6, 9) and (12, 39).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 9) ÷ (12 − 6) = 30 ÷ 6 = 5.

  8. 8. Find the gradient of the line passing through (5, 4) and (9, 8).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 4) ÷ (9 − 5) = 4 ÷ 4 = 1.

  9. 9. Find the gradient of the line passing through (4, 2) and (10, 26).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 2) ÷ (10 − 4) = 24 ÷ 6 = 4.

  10. 10. Find the gradient of the line passing through (4, 1) and (8, 25).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 1) ÷ (8 − 4) = 24 ÷ 4 = 6.

  11. 11. Find the gradient of the line passing through (2, 6) and (6, 34).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 6) ÷ (6 − 2) = 28 ÷ 4 = 7.

  12. 12. Find the gradient of the line passing through (2, 9) and (3, 14).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (3 − 2) = 5 ÷ 1 = 5.

12 questions · Seed 104744 · Age guidance, not curriculum certification