The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
\[m = \frac{y_2 - y_1}{x_2 - x_1}.\]
In this case, we have $P(-2,7)$ and $Q(4,y)$, so the slope of the line passing through these points is
\[m = \frac{y - 7}{4 - (-2)} = \frac{y - 7}{6}.\]
We want this slope to be $-\frac{3}{2}$, so we have the equation
\[\frac{y - 7}{6} = -\frac{3}{2}.\]
Simplifying, we find $y - 7 = -9$, so $y = \boxed{-2}.$
The answer is: -2
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
For what value of $y$ is the slope of the line passing through points $P(-2,7)$ and $Q(4,y)$ equal to $-\frac{3}{2}$?

### Answer:
