AlgebraHardValue of a line-defined function at another input
Algebra practice question
The graph of the linear function f in the xy-plane has slope −3 and passes through the point (2, 4). What is the value of f(−1)?
Answer: 13
f(x) = −3x + b, and 4 = −3(2) + b gives b = 10. So f(x) = −3x + 10, and f(−1) = 3 + 10 = 13.
Common wrong answers
- If you answered 1
- 1 is f(3), moving one step forward from x = 2 instead of three steps back to x = −1.
- If you answered 7
- 7 is −3(−1) + 4, using the given y-value 4 as the intercept; the intercept is 10.
- If you answered -13
- −13 has the wrong sign: −3 × (−1) is +3, and 3 + 10 = 13.
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