AQA · Mathematics · 8300

GCSE Maths: Linear graphs: gradient between points

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Linear graphs: gradient between points (Corbettmaths Video 190), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. What is the formula for calculating the gradient of a line between two points (x₁, y₁) and (x₂, y₂)?

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    Gradient = (y₂ − y₁) ÷ (x₂ − x₁), which is the change in y divided by the change in x.

  2. What is the gradient of the line passing through points (1, 4) and (3, 10)?

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    3. Using gradient = (y₂ − y₁) ÷ (x₂ − x₁) = (10 − 4) ÷ (3 − 1) = 6 ÷ 2 = 3

  3. What is the gradient of the line passing through points (−8, 6) and (0, −2)?

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    −1. Using gradient = (y₂ − y₁) ÷ (x₂ − x₁) = (−2 − 6) ÷ (0 − (−8)) = −8 ÷ 8 = −1

  4. What is the gradient of the line AB where A is (−4, 1) and B is (6, 6)?

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    0.5 or ½. Gradient = (6 − 1) ÷ (6 − (−4)) = 5 ÷ 10 = 0.5

  5. What is the gradient of the line AB where A is (1, 4) and B is (7, 22)?

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    3. Gradient = (22 − 4) ÷ (7 − 1) = 18 ÷ 6 = 3

  6. What is the gradient of the line passing through (3, 2) and (7, 20)?

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    4.5 or 9/2. Gradient = (20 − 2) ÷ (7 − 3) = 18 ÷ 4 = 4.5

  7. What is the gradient of the line passing through (−8, −20) and (−1, 22)?

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    6. Gradient = (22 − (−20)) ÷ (−1 − (−8)) = 42 ÷ 7 = 6

  8. What is the gradient of the line y = 4x + 2?

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    4. In the equation y = mx + c, m is the gradient, so the gradient is 4.

  9. If a line passes through (4, −7) and (8, c) with gradient 3, what is the value of c?

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    5. Using 3 = (c − (−7)) ÷ (8 − 4), so 3 = (c + 7) ÷ 4, therefore c + 7 = 12, and c = 5

  10. If a line passes through (6, −4) and (a, 10) with gradient 2, what is the value of a?

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    13. Using 2 = (10 − (−4)) ÷ (a − 6), so 2 = 14 ÷ (a − 6), therefore a − 6 = 7, and a = 13

  11. What common mistake might a student make when calculating gradient if they divide the horizontal change by the vertical change?

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    They would get the reciprocal of the correct gradient. Gradient must be vertical change (Δy) divided by horizontal change (Δx), not the other way around.

  12. If a line passes through points (m, n) and (p, q) where p = m + 6 and n = q − 18, what is the gradient?

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    −3. Gradient = (q − n) ÷ (p − m) = (q − (q − 18)) ÷ ((m + 6) − m) = 18 ÷ 6 = 3. Since n is below q, gradient = −18 ÷ 6 = −3

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