AlgebraMediumLinear function from a difference in outputs
Algebra practice question
The function g is linear. It is known that g(4) − g(1) = 9 and that g(1) = −2. What is the value of g(7)?
Answer: 16
The output rises by 9 as x goes from 1 to 4, so the slope is 9/3 = 3. From x = 1 to x = 7 is 6 steps: g(7) = g(1) + 6(3) = −2 + 18 = 16.
Common wrong answers
- If you answered 7
- 7 is g(4) = −2 + 9; the question asks for g(7).
- If you answered 19
- 19 comes from adding 3 × 7 to −2 instead of 3 × 6.
- If you answered 25
- 25 comes from adding 9 three times (as if the slope were 9 per unit).
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