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MathsAges 13-15

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 13-15

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (5, 4) and (7, 18).

    5 · 4 · 7 · 18 · Gradient of a line

  2. 2. Find the gradient of the line passing through (1, 9) and (4, 21).

    1 · 9 · 4 · 21 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 5) and (4, 19).

    2 · 5 · 4 · 19 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 3) and (12, 21).

    6 · 3 · 12 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 10) and (9, 35).

    4 · 10 · 9 · 35 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 49).

    3 · 1 · 9 · 49 · Gradient of a line

  7. 7. Find the gradient of the line passing through (2, 8) and (5, 26).

    2 · 8 · 5 · 26 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (5, 30).

    1 · 6 · 5 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 10) and (7, 16).

    4 · 10 · 7 · 16 · Gradient of a line

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

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

  11. 11. Find the gradient of the line passing through (3, 7) and (5, 15).

    3 · 7 · 5 · 15 · Gradient of a line

  12. 12. Find the gradient of the line passing through (8, 10) and (13, 35).

    8 · 10 · 13 · 35 · Gradient of a line
12 questions · Seed 104734 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (5, 4) and (7, 18).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 4) ÷ (7 − 5) = 14 ÷ 2 = 7.

  2. 2. Find the gradient of the line passing through (1, 9) and (4, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (4 − 1) = 12 ÷ 3 = 4.

  3. 3. Find the gradient of the line passing through (2, 5) and (4, 19).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 5) ÷ (4 − 2) = 14 ÷ 2 = 7.

  4. 4. Find the gradient of the line passing through (6, 3) and (12, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 3) ÷ (12 − 6) = 18 ÷ 6 = 3.

  5. 5. Find the gradient of the line passing through (4, 10) and (9, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 10) ÷ (9 − 4) = 25 ÷ 5 = 5.

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 49).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (49 − 1) ÷ (9 − 3) = 48 ÷ 6 = 8.

  7. 7. Find the gradient of the line passing through (2, 8) and (5, 26).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (5 − 2) = 18 ÷ 3 = 6.

  8. 8. Find the gradient of the line passing through (1, 6) and (5, 30).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 6) ÷ (5 − 1) = 24 ÷ 4 = 6.

  9. 9. Find the gradient of the line passing through (4, 10) and (7, 16).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 10) ÷ (7 − 4) = 6 ÷ 3 = 2.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 2) ÷ (4 − 2) = 10 ÷ 2 = 5.

  11. 11. Find the gradient of the line passing through (3, 7) and (5, 15).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 7) ÷ (5 − 3) = 8 ÷ 2 = 4.

  12. 12. Find the gradient of the line passing through (8, 10) and (13, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 10) ÷ (13 − 8) = 25 ÷ 5 = 5.

12 questions · Seed 104734 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Gradient of a line

Take your time. Show your thinking.

  1. 1. Find the gradient of the line passing through (5, 4) and (7, 18).

    5 · 4 · 7 · 18 · Gradient of a line

  2. 2. Find the gradient of the line passing through (1, 9) and (4, 21).

    1 · 9 · 4 · 21 · Gradient of a line

  3. 3. Find the gradient of the line passing through (2, 5) and (4, 19).

    2 · 5 · 4 · 19 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 3) and (12, 21).

    6 · 3 · 12 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (4, 10) and (9, 35).

    4 · 10 · 9 · 35 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 49).

    3 · 1 · 9 · 49 · Gradient of a line

  7. 7. Find the gradient of the line passing through (2, 8) and (5, 26).

    2 · 8 · 5 · 26 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (5, 30).

    1 · 6 · 5 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (4, 10) and (7, 16).

    4 · 10 · 7 · 16 · Gradient of a line

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

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

  11. 11. Find the gradient of the line passing through (3, 7) and (5, 15).

    3 · 7 · 5 · 15 · Gradient of a line

  12. 12. Find the gradient of the line passing through (8, 10) and (13, 35).

    8 · 10 · 13 · 35 · Gradient of a line
12 questions · Seed 104734 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Gradient of a line

Answers and reasoning. Review before teaching.

  1. 1. Find the gradient of the line passing through (5, 4) and (7, 18).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 4) ÷ (7 − 5) = 14 ÷ 2 = 7.

  2. 2. Find the gradient of the line passing through (1, 9) and (4, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (4 − 1) = 12 ÷ 3 = 4.

  3. 3. Find the gradient of the line passing through (2, 5) and (4, 19).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 5) ÷ (4 − 2) = 14 ÷ 2 = 7.

  4. 4. Find the gradient of the line passing through (6, 3) and (12, 21).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 3) ÷ (12 − 6) = 18 ÷ 6 = 3.

  5. 5. Find the gradient of the line passing through (4, 10) and (9, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 10) ÷ (9 − 4) = 25 ÷ 5 = 5.

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 49).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (49 − 1) ÷ (9 − 3) = 48 ÷ 6 = 8.

  7. 7. Find the gradient of the line passing through (2, 8) and (5, 26).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (5 − 2) = 18 ÷ 3 = 6.

  8. 8. Find the gradient of the line passing through (1, 6) and (5, 30).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 6) ÷ (5 − 1) = 24 ÷ 4 = 6.

  9. 9. Find the gradient of the line passing through (4, 10) and (7, 16).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (16 − 10) ÷ (7 − 4) = 6 ÷ 3 = 2.

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

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 2) ÷ (4 − 2) = 10 ÷ 2 = 5.

  11. 11. Find the gradient of the line passing through (3, 7) and (5, 15).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 7) ÷ (5 − 3) = 8 ÷ 2 = 4.

  12. 12. Find the gradient of the line passing through (8, 10) and (13, 35).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (35 − 10) ÷ (13 − 8) = 25 ÷ 5 = 5.

12 questions · Seed 104734 · Age guidance, not curriculum certification