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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 (4, 5) and (5, 7).

    4 · 5 · 5 · 7 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (7, 13).

    5 · 9 · 7 · 13 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 1) and (9, 19).

    7 · 1 · 9 · 19 · Gradient of a line

  4. 4. Find the gradient of the line passing through (7, 9) and (9, 21).

    7 · 9 · 9 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 5) and (14, 29).

    8 · 5 · 14 · 29 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 9) and (9, 14).

    4 · 9 · 9 · 14 · Gradient of a line

  7. 7. Find the gradient of the line passing through (5, 6) and (8, 12).

    5 · 6 · 8 · 12 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 1) and (7, 55).

    1 · 1 · 7 · 55 · Gradient of a line

  9. 9. Find the gradient of the line passing through (5, 2) and (7, 8).

    5 · 2 · 7 · 8 · Gradient of a line

  10. 10. Find the gradient of the line passing through (3, 9) and (7, 41).

    3 · 9 · 7 · 41 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 8) and (11, 26).

    5 · 8 · 11 · 26 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 4) and (7, 34).

    1 · 4 · 7 · 34 · Gradient of a line
12 questions · Seed 104739 · 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 (4, 5) and (5, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 5) ÷ (5 − 4) = 2 ÷ 1 = 2.

  2. 2. Find the gradient of the line passing through (5, 9) and (7, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 9) ÷ (7 − 5) = 4 ÷ 2 = 2.

  3. 3. Find the gradient of the line passing through (7, 1) and (9, 19).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 1) ÷ (9 − 7) = 18 ÷ 2 = 9.

  4. 4. Find the gradient of the line passing through (7, 9) and (9, 21).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (9 − 7) = 12 ÷ 2 = 6.

  5. 5. Find the gradient of the line passing through (8, 5) and (14, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (14 − 8) = 24 ÷ 6 = 4.

  6. 6. Find the gradient of the line passing through (4, 9) and (9, 14).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (9 − 4) = 5 ÷ 5 = 1.

  7. 7. Find the gradient of the line passing through (5, 6) and (8, 12).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 6) ÷ (8 − 5) = 6 ÷ 3 = 2.

  8. 8. Find the gradient of the line passing through (1, 1) and (7, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 1) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (5, 2) and (7, 8).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 2) ÷ (7 − 5) = 6 ÷ 2 = 3.

  10. 10. Find the gradient of the line passing through (3, 9) and (7, 41).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (41 − 9) ÷ (7 − 3) = 32 ÷ 4 = 8.

  11. 11. Find the gradient of the line passing through (5, 8) and (11, 26).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (11 − 5) = 18 ÷ 6 = 3.

  12. 12. Find the gradient of the line passing through (1, 4) and (7, 34).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 4) ÷ (7 − 1) = 30 ÷ 6 = 5.

12 questions · Seed 104739 · 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 (4, 5) and (5, 7).

    4 · 5 · 5 · 7 · Gradient of a line

  2. 2. Find the gradient of the line passing through (5, 9) and (7, 13).

    5 · 9 · 7 · 13 · Gradient of a line

  3. 3. Find the gradient of the line passing through (7, 1) and (9, 19).

    7 · 1 · 9 · 19 · Gradient of a line

  4. 4. Find the gradient of the line passing through (7, 9) and (9, 21).

    7 · 9 · 9 · 21 · Gradient of a line

  5. 5. Find the gradient of the line passing through (8, 5) and (14, 29).

    8 · 5 · 14 · 29 · Gradient of a line

  6. 6. Find the gradient of the line passing through (4, 9) and (9, 14).

    4 · 9 · 9 · 14 · Gradient of a line

  7. 7. Find the gradient of the line passing through (5, 6) and (8, 12).

    5 · 6 · 8 · 12 · Gradient of a line

  8. 8. Find the gradient of the line passing through (1, 1) and (7, 55).

    1 · 1 · 7 · 55 · Gradient of a line

  9. 9. Find the gradient of the line passing through (5, 2) and (7, 8).

    5 · 2 · 7 · 8 · Gradient of a line

  10. 10. Find the gradient of the line passing through (3, 9) and (7, 41).

    3 · 9 · 7 · 41 · Gradient of a line

  11. 11. Find the gradient of the line passing through (5, 8) and (11, 26).

    5 · 8 · 11 · 26 · Gradient of a line

  12. 12. Find the gradient of the line passing through (1, 4) and (7, 34).

    1 · 4 · 7 · 34 · Gradient of a line
12 questions · Seed 104739 · 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 (4, 5) and (5, 7).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (7 − 5) ÷ (5 − 4) = 2 ÷ 1 = 2.

  2. 2. Find the gradient of the line passing through (5, 9) and (7, 13).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 9) ÷ (7 − 5) = 4 ÷ 2 = 2.

  3. 3. Find the gradient of the line passing through (7, 1) and (9, 19).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (19 − 1) ÷ (9 − 7) = 18 ÷ 2 = 9.

  4. 4. Find the gradient of the line passing through (7, 9) and (9, 21).

    6

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (21 − 9) ÷ (9 − 7) = 12 ÷ 2 = 6.

  5. 5. Find the gradient of the line passing through (8, 5) and (14, 29).

    4

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (29 − 5) ÷ (14 − 8) = 24 ÷ 6 = 4.

  6. 6. Find the gradient of the line passing through (4, 9) and (9, 14).

    1

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (14 − 9) ÷ (9 − 4) = 5 ÷ 5 = 1.

  7. 7. Find the gradient of the line passing through (5, 6) and (8, 12).

    2

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (12 − 6) ÷ (8 − 5) = 6 ÷ 3 = 2.

  8. 8. Find the gradient of the line passing through (1, 1) and (7, 55).

    9

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (55 − 1) ÷ (7 − 1) = 54 ÷ 6 = 9.

  9. 9. Find the gradient of the line passing through (5, 2) and (7, 8).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 2) ÷ (7 − 5) = 6 ÷ 2 = 3.

  10. 10. Find the gradient of the line passing through (3, 9) and (7, 41).

    8

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (41 − 9) ÷ (7 − 3) = 32 ÷ 4 = 8.

  11. 11. Find the gradient of the line passing through (5, 8) and (11, 26).

    3

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (26 − 8) ÷ (11 − 5) = 18 ÷ 6 = 3.

  12. 12. Find the gradient of the line passing through (1, 4) and (7, 34).

    5

    Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (34 − 4) ÷ (7 − 1) = 30 ÷ 6 = 5.

12 questions · Seed 104739 · Age guidance, not curriculum certification