Answer
7
Work Step by Step
For A, B, and C to be collinear, the slopes of $\overline{AB}$ and $\overline{BC}$ must be equal.
Slope of $\overline{AB}$: $\frac{5-3}{4-1}=\frac{2}{3}$
Slope of $\overline{BC}$: $\frac{a-5}{a-4}$
$\frac{2}{3}=\frac{a-5}{a-4}$
$2(a-4)=3(a-5)$
$2a-8=3a-15$
$a=7$
