= 6 + b

February 22, 2026

= 6 + b

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Question: A zoologist models the number of observed behaviors per day as $ y = 2x + b $, where $ x $ is the number of hours spent in the field. If 3 hours of observation yield 11 total behaviors, find the $ y $-intercept of the line.
Solution: We are given a point $ (3, 11) $ lies on the line $ y = 2x + b $. Substitute $ x = 3 $ and $ y = 11 $:
= 2(3) + b
b = 5
The $ y $-intercept is the point $ (0, b) $, so it is $\boxed{5}$.
Question: A science educator uses a function $ h(x) = x^2 - 4x + c $ to model student performance, and finds that the minimum score occurs at $ x = 2 $. What value of $ c $ ensures $ h(2) = 3 $?

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