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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 (6, 8) and (12, 20).

    6 · 8 · 12 · 20 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 15).

    5 · 9 · 11 · 15 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 3) and (6, 13).

    1 · 3 · 6 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (8, 21).

    4 · 5 · 8 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 7) and (6, 23).

    2 · 7 · 6 · 23 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 3) and (12, 27).

    8 · 3 · 12 · 27 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 5) and (4, 8).

    3 · 5 · 4 · 8 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 8) and (13, 56).

    7 · 8 · 13 · 56 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 5) and (5, 9).

    3 · 5 · 5 · 9 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 3) and (9, 13).

    4 · 3 · 9 · 13 · Gradient of a line

  11. 11. Find the gradient of the line passing through (6, 4) and (7, 9).

    6 · 4 · 7 · 9 · Gradient of a line

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

    1 · 1 · 4 · 7 · Gradient of a line
12 questions · Seed 104736 · 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 (6, 8) and (12, 20).

    2

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

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 9) ÷ (11 − 5) = 6 ÷ 6 = 1.

  3. 3. Find the gradient of the line passing through (1, 3) and (6, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 3) ÷ (6 − 1) = 10 ÷ 5 = 2.

  4. 4. Find the gradient of the line passing through (4, 5) and (8, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (8 − 4) = 16 ÷ 4 = 4.

  5. 5. Find the gradient of the line passing through (2, 7) and (6, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 7) ÷ (6 − 2) = 16 ÷ 4 = 4.

  6. 6. Find the gradient of the line passing through (8, 3) and (12, 27).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 3) ÷ (12 − 8) = 24 ÷ 4 = 6.

  7. 7. Find the gradient of the line passing through (3, 5) and (4, 8).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 5) ÷ (4 − 3) = 3 ÷ 1 = 3.

  8. 8. Find the gradient of the line passing through (7, 8) and (13, 56).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (56 − 8) ÷ (13 − 7) = 48 ÷ 6 = 8.

  9. 9. Find the gradient of the line passing through (3, 5) and (5, 9).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 5) ÷ (5 − 3) = 4 ÷ 2 = 2.

  10. 10. Find the gradient of the line passing through (4, 3) and (9, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 3) ÷ (9 − 4) = 10 ÷ 5 = 2.

  11. 11. Find the gradient of the line passing through (6, 4) and (7, 9).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 4) ÷ (7 − 6) = 5 ÷ 1 = 5.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (4 − 1) = 6 ÷ 3 = 2.

12 questions · Seed 104736 · 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 (6, 8) and (12, 20).

    6 · 8 · 12 · 20 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 15).

    5 · 9 · 11 · 15 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 3) and (6, 13).

    1 · 3 · 6 · 13 · Gradient of a line

  4. 4. Find the gradient of the line passing through (4, 5) and (8, 21).

    4 · 5 · 8 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 7) and (6, 23).

    2 · 7 · 6 · 23 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 3) and (12, 27).

    8 · 3 · 12 · 27 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 5) and (4, 8).

    3 · 5 · 4 · 8 · Gradient of a line

  8. 8. Find the gradient of the line passing through (7, 8) and (13, 56).

    7 · 8 · 13 · 56 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 5) and (5, 9).

    3 · 5 · 5 · 9 · Gradient of a line

  10. 10. Find the gradient of the line passing through (4, 3) and (9, 13).

    4 · 3 · 9 · 13 · Gradient of a line

  11. 11. Find the gradient of the line passing through (6, 4) and (7, 9).

    6 · 4 · 7 · 9 · Gradient of a line

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

    1 · 1 · 4 · 7 · Gradient of a line
12 questions · Seed 104736 · 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 (6, 8) and (12, 20).

    2

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

  2. 2. Find the gradient of the line passing through (5, 9) and (11, 15).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (15 − 9) ÷ (11 − 5) = 6 ÷ 6 = 1.

  3. 3. Find the gradient of the line passing through (1, 3) and (6, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 3) ÷ (6 − 1) = 10 ÷ 5 = 2.

  4. 4. Find the gradient of the line passing through (4, 5) and (8, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 5) ÷ (8 − 4) = 16 ÷ 4 = 4.

  5. 5. Find the gradient of the line passing through (2, 7) and (6, 23).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (23 − 7) ÷ (6 − 2) = 16 ÷ 4 = 4.

  6. 6. Find the gradient of the line passing through (8, 3) and (12, 27).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 3) ÷ (12 − 8) = 24 ÷ 4 = 6.

  7. 7. Find the gradient of the line passing through (3, 5) and (4, 8).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 5) ÷ (4 − 3) = 3 ÷ 1 = 3.

  8. 8. Find the gradient of the line passing through (7, 8) and (13, 56).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (56 − 8) ÷ (13 − 7) = 48 ÷ 6 = 8.

  9. 9. Find the gradient of the line passing through (3, 5) and (5, 9).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 5) ÷ (5 − 3) = 4 ÷ 2 = 2.

  10. 10. Find the gradient of the line passing through (4, 3) and (9, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 3) ÷ (9 − 4) = 10 ÷ 5 = 2.

  11. 11. Find the gradient of the line passing through (6, 4) and (7, 9).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (9 − 4) ÷ (7 − 6) = 5 ÷ 1 = 5.

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

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (4 − 1) = 6 ÷ 3 = 2.

12 questions · Seed 104736 · Age guidance, not curriculum certification