AlgebraVery hardDifference of two outputs from the slope
Algebra practice question
A linear function f satisfies f(2) = 9 and f(5) = 21. What is the value of f(8) − f(6)?
Answer: 8
The slope is (21 − 9)/(5 − 2) = 4, so f rises by 4 for each unit of x. From x = 6 to x = 8 is 2 units: 4 × 2 = 8.
Common wrong answers
- If you answered 2
- 2 is the width of the interval, not the change in f.
- If you answered 4
- 4 is the change per ONE unit of x; the interval is 2 units.
- If you answered 12
- 12 is the change from x = 2 to x = 5, not from 6 to 8.
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