ANSWER
p = -10
EXPLANATION
The formula for the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this problem we know the slope, one point and the x-coordinate of the other point. We have to find its y-coordinate:
[tex]-\frac{3}{2}=\frac{p-2}{3-(-5)}[/tex]Solving for p:
[tex]\begin{gathered} -\frac{3}{2}=\frac{p-2}{3+5} \\ -\frac{3}{2}=\frac{p-2}{8} \\ p-2=-\frac{3}{2}\cdot8 \\ p-2=-12 \\ p=-12+2 \\ p=-10 \end{gathered}[/tex]