AQA · Mathematics · 8300

GCSE Maths: Linear graphs: gradient of a line

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Linear graphs: gradient of a line (Corbettmaths Video 189), 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 gradient of the line passing through (1, 4) and (3, 10)?

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    3. Change in y = 10 − 4 = 6; change in x = 3 − 1 = 2; gradient = 6 ÷ 2 = 3.

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

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    −1. Change in y = −2 − 6 = −8; change in x = 0 − (−8) = 8; gradient = −8 ÷ 8 = −1.

  3. What is the gradient of the line passing through (−4, 1) and (6, 6)?

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    0.5 or ½. Change in y = 6 − 1 = 5; change in x = 6 − (−4) = 10; gradient = 5 ÷ 10 = 0.5.

  4. What is the gradient of the line passing through (1, 4) and (7, 22)?

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    3. Change in y = 22 − 4 = 18; change in x = 7 − 1 = 6; gradient = 18 ÷ 6 = 3.

  5. What is the gradient of the line passing through (−4, 5) and (−1, 11)?

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    2. Change in y = 11 − 5 = 6; change in x = −1 − (−4) = 3; gradient = 6 ÷ 3 = 2.

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

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    4.5 or 9/2. Change in y = 20 − 2 = 18; change in x = 7 − 3 = 4; gradient = 18 ÷ 4 = 4.5.

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

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    5. Using gradient = (c − (−7)) ÷ (8 − 4) = 3, so (c + 7) ÷ 4 = 3, giving c + 7 = 12, thus c = 5.

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

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    13. Using gradient = (10 − (−4)) ÷ (a − 6) = 2, so 14 ÷ (a − 6) = 2, giving a − 6 = 7, thus a = 13.

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

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    4. In the form y = mx + c, the coefficient of x is the gradient.

  10. What is the gradient of the line passing through (120, 1100) and (200, 3500)?

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    30. Change in y = 3500 − 1100 = 2400; change in x = 200 − 120 = 80; gradient = 2400 ÷ 80 = 30.

  11. If a line passes through (4, a) and (8, 1) and has gradient ¾, what is the value of a?

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    −2. Using gradient = (1 − a) ÷ (8 − 4) = ¾, so (1 − a) ÷ 4 = ¾, giving 1 − a = 3, thus a = −2.

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