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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 (1, 7) and (3, 25).

    1 · 7 · 3 · 25 · Gradient of a line

  2. 2. Find the gradient of the line passing through (2, 3) and (8, 45).

    2 · 3 · 8 · 45 · Gradient of a line

  3. 3. Find the gradient of the line passing through (6, 6) and (7, 13).

    6 · 6 · 7 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 5) and (3, 7).

    1 · 5 · 3 · 7 · Gradient of a line

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 21).

    5 · 1 · 10 · 21 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 8) and (7, 20).

    1 · 8 · 7 · 20 · Gradient of a line

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

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

  8. 8. Find the gradient of the line passing through (7, 2) and (13, 50).

    7 · 2 · 13 · 50 · Gradient of a line

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

    3 · 4 · 4 · 11 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 1) and (9, 7).

    6 · 1 · 9 · 7 · Gradient of a line

  11. 11. Find the gradient of the line passing through (1, 2) and (6, 22).

    1 · 2 · 6 · 22 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 6) and (6, 10).

    2 · 6 · 6 · 10 · Gradient of a line
12 questions · Seed 104745 · 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 (1, 7) and (3, 25).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (3 − 1) = 18 ÷ 2 = 9.

  2. 2. Find the gradient of the line passing through (2, 3) and (8, 45).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 3) ÷ (8 − 2) = 42 ÷ 6 = 7.

  3. 3. Find the gradient of the line passing through (6, 6) and (7, 13).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 6) ÷ (7 − 6) = 7 ÷ 1 = 7.

  4. 4. Find the gradient of the line passing through (1, 5) and (3, 7).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 5) ÷ (3 − 1) = 2 ÷ 2 = 1.

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 1) ÷ (10 − 5) = 20 ÷ 5 = 4.

  6. 6. Find the gradient of the line passing through (1, 8) and (7, 20).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 8) ÷ (7 − 1) = 12 ÷ 6 = 2.

  7. 7. 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.

  8. 8. Find the gradient of the line passing through (7, 2) and (13, 50).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (50 − 2) ÷ (13 − 7) = 48 ÷ 6 = 8.

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

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 4) ÷ (4 − 3) = 7 ÷ 1 = 7.

  10. 10. Find the gradient of the line passing through (6, 1) and (9, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (9 − 6) = 6 ÷ 3 = 2.

  11. 11. Find the gradient of the line passing through (1, 2) and (6, 22).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 2) ÷ (6 − 1) = 20 ÷ 5 = 4.

  12. 12. Find the gradient of the line passing through (2, 6) and (6, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 6) ÷ (6 − 2) = 4 ÷ 4 = 1.

12 questions · Seed 104745 · 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 (1, 7) and (3, 25).

    1 · 7 · 3 · 25 · Gradient of a line

  2. 2. Find the gradient of the line passing through (2, 3) and (8, 45).

    2 · 3 · 8 · 45 · Gradient of a line

  3. 3. Find the gradient of the line passing through (6, 6) and (7, 13).

    6 · 6 · 7 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (1, 5) and (3, 7).

    1 · 5 · 3 · 7 · Gradient of a line

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 21).

    5 · 1 · 10 · 21 · Gradient of a line

  6. 6. Find the gradient of the line passing through (1, 8) and (7, 20).

    1 · 8 · 7 · 20 · Gradient of a line

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

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

  8. 8. Find the gradient of the line passing through (7, 2) and (13, 50).

    7 · 2 · 13 · 50 · Gradient of a line

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

    3 · 4 · 4 · 11 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 1) and (9, 7).

    6 · 1 · 9 · 7 · Gradient of a line

  11. 11. Find the gradient of the line passing through (1, 2) and (6, 22).

    1 · 2 · 6 · 22 · Gradient of a line

  12. 12. Find the gradient of the line passing through (2, 6) and (6, 10).

    2 · 6 · 6 · 10 · Gradient of a line
12 questions · Seed 104745 · 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 (1, 7) and (3, 25).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 7) ÷ (3 − 1) = 18 ÷ 2 = 9.

  2. 2. Find the gradient of the line passing through (2, 3) and (8, 45).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 3) ÷ (8 − 2) = 42 ÷ 6 = 7.

  3. 3. Find the gradient of the line passing through (6, 6) and (7, 13).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 6) ÷ (7 − 6) = 7 ÷ 1 = 7.

  4. 4. Find the gradient of the line passing through (1, 5) and (3, 7).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 5) ÷ (3 − 1) = 2 ÷ 2 = 1.

  5. 5. Find the gradient of the line passing through (5, 1) and (10, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 1) ÷ (10 − 5) = 20 ÷ 5 = 4.

  6. 6. Find the gradient of the line passing through (1, 8) and (7, 20).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (20 − 8) ÷ (7 − 1) = 12 ÷ 6 = 2.

  7. 7. 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.

  8. 8. Find the gradient of the line passing through (7, 2) and (13, 50).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (50 − 2) ÷ (13 − 7) = 48 ÷ 6 = 8.

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

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 4) ÷ (4 − 3) = 7 ÷ 1 = 7.

  10. 10. Find the gradient of the line passing through (6, 1) and (9, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (9 − 6) = 6 ÷ 3 = 2.

  11. 11. Find the gradient of the line passing through (1, 2) and (6, 22).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 2) ÷ (6 − 1) = 20 ÷ 5 = 4.

  12. 12. Find the gradient of the line passing through (2, 6) and (6, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 6) ÷ (6 − 2) = 4 ÷ 4 = 1.

12 questions · Seed 104745 · Age guidance, not curriculum certification