AlgebraHardExtending a linear function from two points
Algebra practice question
The graph of the linear function f in the xy-plane passes through the points (1, 3) and (3, 11). What is the value of f(10)?
Answer: 39
Slope: (11 − 3)/(3 − 1) = 4. Then f(x) = 4x + b with 3 = 4(1) + b, so b = −1 and f(x) = 4x − 1. f(10) = 40 − 1 = 39.
Common wrong answers
- If you answered 31
- 31 is 11 + 4 × 5, moving 5 steps from x = 3 to x = 8 — but x = 10 is 7 steps from x = 3: 11 + 28 = 39.
- If you answered 40
- 40 is 4 × 10, the slope times x, without the intercept −1.
- If you answered 43
- 43 uses b = +3 (the y-value of the first point) as the intercept; the intercept is −1.
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