AlgebraVery hardSlope of a linear function that swaps two values
Algebra practice question
A linear function f satisfies f(a) = b and f(b) = a, where a and b are distinct constants. What is the slope of the graph of f?
Answer: -1
Slope = (f(b) − f(a))/(b − a) = (a − b)/(b − a) = −1.
Common wrong answers
- If you answered 0
- 0 would need f(a) = f(b), but a ≠ b.
- If you answered 1
- 1 has the wrong sign: the rise is a − b while the run is b − a.
- If you answered -2
- −2 doubles the slope without reason.
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