If $f(x) = ax + b$ with $f(1) = 5$ and $f(3) = 11$, find $a$ and $b$.
A$a = 2, b = 3$
B$a = 1, b = 4$
C$a = 3, b = 2$
D$a = 4, b = 1$
Answer & Solution
Correct answer: C. $a = 3, b = 2$
From $f(1) = 5$: $a + b = 5$. From $f(3) = 11$: $3a + b = 11$. Subtracting: $2a = 6 \Rightarrow a = 3$, so $b = 2$.
Check: $f(1) = 3 + 2 = 5$ ✓, $f(3) = 9 + 2 = 11$ ✓.
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