Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 A line rises 10 and runs 5. Find the gradient.
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10 ÷ 5 = 2.
2 What is the gradient of a horizontal line?
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0.
3 A line goes downhill from left to right. Is its gradient positive or negative?
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Negative.
Level 2 · Core
4 Find the gradient of the line through (1, 1) and (4, 7).
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6 ÷ 3 = 2.
5 Find the gradient of the line through (0, 2) and (5, 2).
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Rise = 0, so m = 0 (a horizontal line).
6 What is the gradient of a vertical line?
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Undefined.
Level 3 · Challenge
7 Find the gradient of the line through (−1, 4) and (3, −4).
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rise −8, run 4 → m = −2.
8 Find the gradient of the line through (2, 5) and (6, −3).
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rise = −3 − 5 = −8, run = 4 → m = −2.
9 A graph shows cost rising $45 over 3 items. What is the gradient, in dollars per item?
Show worked solution
45 ÷ 3 = $15 per item.