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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 (3, 3) and (7, 19).

    3 · 3 · 7 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 2) and (7, 17).

    4 · 2 · 7 · 17 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 6) and (9, 36).

    4 · 6 · 9 · 36 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 7) and (6, 31).

    2 · 7 · 6 · 31 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 1) and (11, 7).

    8 · 1 · 11 · 7 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 9) and (14, 27).

    8 · 9 · 14 · 27 · Gradient of a line

  7. 7. Find the gradient of the line passing through (5, 7) and (8, 19).

    5 · 7 · 8 · 19 · Gradient of a line

  8. 8. Find the gradient of the line passing through (5, 10) and (7, 18).

    5 · 10 · 7 · 18 · Gradient of a line

  9. 9. Find the gradient of the line passing through (6, 1) and (11, 46).

    6 · 1 · 11 · 46 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 6) and (9, 27).

    6 · 6 · 9 · 27 · Gradient of a line

  11. 11. Find the gradient of the line passing through (3, 4) and (6, 25).

    3 · 4 · 6 · 25 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 6) and (8, 42).

    4 · 6 · 8 · 42 · Gradient of a line
12 questions · Seed 104729 · 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 (3, 3) and (7, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 3) ÷ (7 − 3) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (4, 2) and (7, 17).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 2) ÷ (7 − 4) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (4, 6) and (9, 36).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 6) ÷ (9 − 4) = 30 ÷ 5 = 6.

  4. 4. Find the gradient of the line passing through (2, 7) and (6, 31).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 7) ÷ (6 − 2) = 24 ÷ 4 = 6.

  5. 5. Find the gradient of the line passing through (8, 1) and (11, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (11 − 8) = 6 ÷ 3 = 2.

  6. 6. Find the gradient of the line passing through (8, 9) and (14, 27).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 9) ÷ (14 − 8) = 18 ÷ 6 = 3.

  7. 7. Find the gradient of the line passing through (5, 7) and (8, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (8 − 5) = 12 ÷ 3 = 4.

  8. 8. Find the gradient of the line passing through (5, 10) and (7, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 10) ÷ (7 − 5) = 8 ÷ 2 = 4.

  9. 9. Find the gradient of the line passing through (6, 1) and (11, 46).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 1) ÷ (11 − 6) = 45 ÷ 5 = 9.

  10. 10. Find the gradient of the line passing through (6, 6) and (9, 27).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 6) ÷ (9 − 6) = 21 ÷ 3 = 7.

  11. 11. Find the gradient of the line passing through (3, 4) and (6, 25).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 4) ÷ (6 − 3) = 21 ÷ 3 = 7.

  12. 12. Find the gradient of the line passing through (4, 6) and (8, 42).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (42 − 6) ÷ (8 − 4) = 36 ÷ 4 = 9.

12 questions · Seed 104729 · 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 (3, 3) and (7, 19).

    3 · 3 · 7 · 19 · Gradient of a line

  2. 2. Find the gradient of the line passing through (4, 2) and (7, 17).

    4 · 2 · 7 · 17 · Gradient of a line

  3. 3. Find the gradient of the line passing through (4, 6) and (9, 36).

    4 · 6 · 9 · 36 · Gradient of a line

  4. 4. Find the gradient of the line passing through (2, 7) and (6, 31).

    2 · 7 · 6 · 31 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 1) and (11, 7).

    8 · 1 · 11 · 7 · Gradient of a line

  6. 6. Find the gradient of the line passing through (8, 9) and (14, 27).

    8 · 9 · 14 · 27 · Gradient of a line

  7. 7. Find the gradient of the line passing through (5, 7) and (8, 19).

    5 · 7 · 8 · 19 · Gradient of a line

  8. 8. Find the gradient of the line passing through (5, 10) and (7, 18).

    5 · 10 · 7 · 18 · Gradient of a line

  9. 9. Find the gradient of the line passing through (6, 1) and (11, 46).

    6 · 1 · 11 · 46 · Gradient of a line

  10. 10. Find the gradient of the line passing through (6, 6) and (9, 27).

    6 · 6 · 9 · 27 · Gradient of a line

  11. 11. Find the gradient of the line passing through (3, 4) and (6, 25).

    3 · 4 · 6 · 25 · Gradient of a line

  12. 12. Find the gradient of the line passing through (4, 6) and (8, 42).

    4 · 6 · 8 · 42 · Gradient of a line
12 questions · Seed 104729 · 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 (3, 3) and (7, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 3) ÷ (7 − 3) = 16 ÷ 4 = 4.

  2. 2. Find the gradient of the line passing through (4, 2) and (7, 17).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (17 − 2) ÷ (7 − 4) = 15 ÷ 3 = 5.

  3. 3. Find the gradient of the line passing through (4, 6) and (9, 36).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (36 − 6) ÷ (9 − 4) = 30 ÷ 5 = 6.

  4. 4. Find the gradient of the line passing through (2, 7) and (6, 31).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (31 − 7) ÷ (6 − 2) = 24 ÷ 4 = 6.

  5. 5. Find the gradient of the line passing through (8, 1) and (11, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 1) ÷ (11 − 8) = 6 ÷ 3 = 2.

  6. 6. Find the gradient of the line passing through (8, 9) and (14, 27).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 9) ÷ (14 − 8) = 18 ÷ 6 = 3.

  7. 7. Find the gradient of the line passing through (5, 7) and (8, 19).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 7) ÷ (8 − 5) = 12 ÷ 3 = 4.

  8. 8. Find the gradient of the line passing through (5, 10) and (7, 18).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (18 − 10) ÷ (7 − 5) = 8 ÷ 2 = 4.

  9. 9. Find the gradient of the line passing through (6, 1) and (11, 46).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (46 − 1) ÷ (11 − 6) = 45 ÷ 5 = 9.

  10. 10. Find the gradient of the line passing through (6, 6) and (9, 27).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (27 − 6) ÷ (9 − 6) = 21 ÷ 3 = 7.

  11. 11. Find the gradient of the line passing through (3, 4) and (6, 25).

    7

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (25 − 4) ÷ (6 − 3) = 21 ÷ 3 = 7.

  12. 12. Find the gradient of the line passing through (4, 6) and (8, 42).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (42 − 6) ÷ (8 − 4) = 36 ÷ 4 = 9.

12 questions · Seed 104729 · Age guidance, not curriculum certification