1. Given points $A(1,-2), B(3,3 x), C(x, 4)$ are on the same straight line, the slope of the line is ( ).
A. -2
B. $\frac{7}{3}$
C. -2 or $\frac{7}{3}$
D. -2 or $\frac{9}{2}$
1. D

Since the necessary and sufficient condition for points $A, B, C$ to be collinear is that the slopes of line $A B$ and line $A C$ are the same, i.e.,
$$
k=\frac{3 x-(-2)}{3-1}=\frac{4-(-2)}{x-1} .
$$

Solving for $x$ gives $x=-2$ or $\frac{7}{3}$. Thus, $k=-2$ or $\frac{9}{2}$.