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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 (2, 5) and (6, 17).

    2 · 5 · 6 · 17 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 3) and (10, 48).

    5 · 3 · 10 · 48 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 10) and (10, 22).

    7 · 10 · 10 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 7) and (11, 32).

    6 · 7 · 11 · 32 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 10) and (10, 14).

    8 · 10 · 10 · 14 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 10) and (8, 34).

    2 · 10 · 8 · 34 · Gradient of a line

  7. 7. Find the gradient of the line passing through (4, 5) and (6, 13).

    4 · 5 · 6 · 13 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 5) and (9, 29).

    3 · 5 · 9 · 29 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 2) and (7, 26).

    3 · 2 · 7 · 26 · Gradient of a line

  10. 10. Find the gradient of the line passing through (5, 2) and (6, 11).

    5 · 2 · 6 · 11 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 4) and (5, 31).

    2 · 4 · 5 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 7) and (4, 10).

    1 · 7 · 4 · 10 · Gradient of a line
12 questions · Seed 104735 · 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 (2, 5) and (6, 17).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 5) ÷ (6 − 2) = 12 ÷ 4 = 3.

  2. 2. Find the gradient of the line passing through (5, 3) and (10, 48).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (48 − 3) ÷ (10 − 5) = 45 ÷ 5 = 9.

  3. 3. Find the gradient of the line passing through (7, 10) and (10, 22).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 10) ÷ (10 − 7) = 12 ÷ 3 = 4.

  4. 4. Find the gradient of the line passing through (6, 7) and (11, 32).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (32 − 7) ÷ (11 − 6) = 25 ÷ 5 = 5.

  5. 5. Find the gradient of the line passing through (8, 10) and (10, 14).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 10) ÷ (10 − 8) = 4 ÷ 2 = 2.

  6. 6. Find the gradient of the line passing through (2, 10) and (8, 34).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 10) ÷ (8 − 2) = 24 ÷ 6 = 4.

  7. 7. Find the gradient of the line passing through (4, 5) and (6, 13).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 5) ÷ (6 − 4) = 8 ÷ 2 = 4.

  8. 8. Find the gradient of the line passing through (3, 5) and (9, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (9 − 3) = 24 ÷ 6 = 4.

  9. 9. Find the gradient of the line passing through (3, 2) and (7, 26).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 2) ÷ (7 − 3) = 24 ÷ 4 = 6.

  10. 10. Find the gradient of the line passing through (5, 2) and (6, 11).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 2) ÷ (6 − 5) = 9 ÷ 1 = 9.

  11. 11. Find the gradient of the line passing through (2, 4) and (5, 31).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 4) ÷ (5 − 2) = 27 ÷ 3 = 9.

  12. 12. Find the gradient of the line passing through (1, 7) and (4, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 7) ÷ (4 − 1) = 3 ÷ 3 = 1.

12 questions · Seed 104735 · 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 (2, 5) and (6, 17).

    2 · 5 · 6 · 17 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 3) and (10, 48).

    5 · 3 · 10 · 48 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 10) and (10, 22).

    7 · 10 · 10 · 22 · Gradient of a line

  4. 4. Find the gradient of the line passing through (6, 7) and (11, 32).

    6 · 7 · 11 · 32 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 10) and (10, 14).

    8 · 10 · 10 · 14 · Gradient of a line

  6. 6. Find the gradient of the line passing through (2, 10) and (8, 34).

    2 · 10 · 8 · 34 · Gradient of a line

  7. 7. Find the gradient of the line passing through (4, 5) and (6, 13).

    4 · 5 · 6 · 13 · Gradient of a line

  8. 8. Find the gradient of the line passing through (3, 5) and (9, 29).

    3 · 5 · 9 · 29 · Gradient of a line

  9. 9. Find the gradient of the line passing through (3, 2) and (7, 26).

    3 · 2 · 7 · 26 · Gradient of a line

  10. 10. Find the gradient of the line passing through (5, 2) and (6, 11).

    5 · 2 · 6 · 11 · Gradient of a line

  11. 11. Find the gradient of the line passing through (2, 4) and (5, 31).

    2 · 4 · 5 · 31 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 7) and (4, 10).

    1 · 7 · 4 · 10 · Gradient of a line
12 questions · Seed 104735 · 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 (2, 5) and (6, 17).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 5) ÷ (6 − 2) = 12 ÷ 4 = 3.

  2. 2. Find the gradient of the line passing through (5, 3) and (10, 48).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (48 − 3) ÷ (10 − 5) = 45 ÷ 5 = 9.

  3. 3. Find the gradient of the line passing through (7, 10) and (10, 22).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (22 − 10) ÷ (10 − 7) = 12 ÷ 3 = 4.

  4. 4. Find the gradient of the line passing through (6, 7) and (11, 32).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (32 − 7) ÷ (11 − 6) = 25 ÷ 5 = 5.

  5. 5. Find the gradient of the line passing through (8, 10) and (10, 14).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 10) ÷ (10 − 8) = 4 ÷ 2 = 2.

  6. 6. Find the gradient of the line passing through (2, 10) and (8, 34).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 10) ÷ (8 − 2) = 24 ÷ 6 = 4.

  7. 7. Find the gradient of the line passing through (4, 5) and (6, 13).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 5) ÷ (6 − 4) = 8 ÷ 2 = 4.

  8. 8. Find the gradient of the line passing through (3, 5) and (9, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (9 − 3) = 24 ÷ 6 = 4.

  9. 9. Find the gradient of the line passing through (3, 2) and (7, 26).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 2) ÷ (7 − 3) = 24 ÷ 4 = 6.

  10. 10. Find the gradient of the line passing through (5, 2) and (6, 11).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 2) ÷ (6 − 5) = 9 ÷ 1 = 9.

  11. 11. Find the gradient of the line passing through (2, 4) and (5, 31).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 4) ÷ (5 − 2) = 27 ÷ 3 = 9.

  12. 12. Find the gradient of the line passing through (1, 7) and (4, 10).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 7) ÷ (4 − 1) = 3 ÷ 3 = 1.

12 questions · Seed 104735 · Age guidance, not curriculum certification