A line passing through the points $(0,-2)$ and $(1,0)$ also passes through the point $(7, b)$. The numerical value of $b$ is
(A) 12
(B) $\frac{9}{2}$
(C) 10
(D) 5
(E) 14
The slope of the line is

$$
\frac{-2-0}{0-1}=2
$$

and its $y$-intercept is -2 (from the first point given), so it has equation $y=2 x-2$.

Substituting in the point $(7, b)$, we obtain $b=2(7)-2=12$.

ANSWER: (A)