AlgebraHardSlope from two function values, then the intercept
Algebra practice question
For a linear function f, f(12) = 13 and f(18) = 17. What is the value of f(0)?
Answer: 5
Slope: (17 − 13)/(18 − 12) = 4/6 = 2/3. From f(12) = 13, moving back 12 units in x lowers f by (2/3)(12) = 8: f(0) = 13 − 8 = 5.
Common wrong answers
- If you answered 1
- 1 comes from a slope of 1 (13 − 12). The slope is 4/6 = 2/3, so the drop from x = 12 to x = 0 is 8.
- If you answered 9
- 9 is 13 − 4, subtracting the change between 12 and 18 instead of the change between 12 and 0 (which is 8).
- If you answered 13
- 13 is f(12), not f(0). The function changes between x = 12 and x = 0.
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