Answer
$b=4$.
Work Step by Step
The slope of the line passing through $(2,-1), (3,2)$ is
$slope=\dfrac{y_1-y_2}{x_1-x_2}=\frac{-1-2}{2-3}= \frac{-3}{-1}= 3$
The slope of the line passing through $(3,2), (b,5)$ is
$slope=\dfrac{y_2-y_3}{x_2-x_3}=\frac{5-2}{b-3}= \frac{3}{b-3}$.
In order for these three points to lie on the same line, we must have equal slopes:
$\frac{3}{b-3}=3$
and then
$b-3=1$
hence,
$b=4$.
