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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 (2, 5) and (7, 50).

    2 · 5 · 7 · 50 · Gradient of a line

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

    6 · 2 · 10 · 6 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 10) and (6, 45).

    1 · 10 · 6 · 45 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 1) and (11, 21).

    6 · 1 · 11 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 6) and (7, 51).

    2 · 6 · 7 · 51 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 7).

    3 · 1 · 9 · 7 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 10) and (6, 13).

    3 · 10 · 6 · 13 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (4, 30).

    1 · 6 · 4 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 3) and (6, 18).

    3 · 3 · 6 · 18 · Gradient of a line

  10. 10. Find the gradient of the line passing through (2, 9) and (8, 39).

    2 · 9 · 8 · 39 · Gradient of a line

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 61).

    4 · 7 · 10 · 61 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 2) and (9, 47).

    4 · 2 · 9 · 47 · Gradient of a line
12 questions · Seed 104732 · 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 (2, 5) and (7, 50).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (50 − 5) ÷ (7 − 2) = 45 ÷ 5 = 9.

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

    1

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

  3. 3. Find the gradient of the line passing through (1, 10) and (6, 45).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 10) ÷ (6 − 1) = 35 ÷ 5 = 7.

  4. 4. Find the gradient of the line passing through (6, 1) and (11, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 1) ÷ (11 − 6) = 20 ÷ 5 = 4.

  5. 5. Find the gradient of the line passing through (2, 6) and (7, 51).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (51 − 6) ÷ (7 − 2) = 45 ÷ 5 = 9.

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 7).

    1

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

  7. 7. Find the gradient of the line passing through (3, 10) and (6, 13).

    1

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

  8. 8. Find the gradient of the line passing through (1, 6) and (4, 30).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 6) ÷ (4 − 1) = 24 ÷ 3 = 8.

  9. 9. Find the gradient of the line passing through (3, 3) and (6, 18).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 3) ÷ (6 − 3) = 15 ÷ 3 = 5.

  10. 10. Find the gradient of the line passing through (2, 9) and (8, 39).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 9) ÷ (8 − 2) = 30 ÷ 6 = 5.

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 61).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (61 − 7) ÷ (10 − 4) = 54 ÷ 6 = 9.

  12. 12. Find the gradient of the line passing through (4, 2) and (9, 47).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (47 − 2) ÷ (9 − 4) = 45 ÷ 5 = 9.

12 questions · Seed 104732 · 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 (2, 5) and (7, 50).

    2 · 5 · 7 · 50 · Gradient of a line

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

    6 · 2 · 10 · 6 · Gradient of a line

  3. 3. Find the gradient of the line passing through (1, 10) and (6, 45).

    1 · 10 · 6 · 45 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 1) and (11, 21).

    6 · 1 · 11 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (2, 6) and (7, 51).

    2 · 6 · 7 · 51 · Gradient of a line

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 7).

    3 · 1 · 9 · 7 · Gradient of a line

  7. 7. Find the gradient of the line passing through (3, 10) and (6, 13).

    3 · 10 · 6 · 13 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 6) and (4, 30).

    1 · 6 · 4 · 30 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 3) and (6, 18).

    3 · 3 · 6 · 18 · Gradient of a line

  10. 10. Find the gradient of the line passing through (2, 9) and (8, 39).

    2 · 9 · 8 · 39 · Gradient of a line

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 61).

    4 · 7 · 10 · 61 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 2) and (9, 47).

    4 · 2 · 9 · 47 · Gradient of a line
12 questions · Seed 104732 · 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 (2, 5) and (7, 50).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (50 − 5) ÷ (7 − 2) = 45 ÷ 5 = 9.

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

    1

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

  3. 3. Find the gradient of the line passing through (1, 10) and (6, 45).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (45 − 10) ÷ (6 − 1) = 35 ÷ 5 = 7.

  4. 4. Find the gradient of the line passing through (6, 1) and (11, 21).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 1) ÷ (11 − 6) = 20 ÷ 5 = 4.

  5. 5. Find the gradient of the line passing through (2, 6) and (7, 51).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (51 − 6) ÷ (7 − 2) = 45 ÷ 5 = 9.

  6. 6. Find the gradient of the line passing through (3, 1) and (9, 7).

    1

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

  7. 7. Find the gradient of the line passing through (3, 10) and (6, 13).

    1

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

  8. 8. Find the gradient of the line passing through (1, 6) and (4, 30).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (30 − 6) ÷ (4 − 1) = 24 ÷ 3 = 8.

  9. 9. Find the gradient of the line passing through (3, 3) and (6, 18).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 3) ÷ (6 − 3) = 15 ÷ 3 = 5.

  10. 10. Find the gradient of the line passing through (2, 9) and (8, 39).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (39 − 9) ÷ (8 − 2) = 30 ÷ 6 = 5.

  11. 11. Find the gradient of the line passing through (4, 7) and (10, 61).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (61 − 7) ÷ (10 − 4) = 54 ÷ 6 = 9.

  12. 12. Find the gradient of the line passing through (4, 2) and (9, 47).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (47 − 2) ÷ (9 − 4) = 45 ÷ 5 = 9.

12 questions · Seed 104732 · Age guidance, not curriculum certification