If the line that passes through the points $(2,7)$ and $(a, 3 a)$ has a slope of 2 , the value of $a$ is
(A) $\frac{5}{2}$
(B) 10
(C) 3
(D) $\frac{11}{5}$
(E) $\frac{12}{5}$
Since the slope of the line through points $(2,7)$ and $(a, 3 a)$ is 2 , then $\frac{3 a-7}{a-2}=2$.

From this, $3 a-7=2(a-2)$ and so $3 a-7=2 a-4$ which gives $a=3$.

ANSWER: (C)