Question

The answer is p = -2/3 and q= -2

Answer 1

$y=\dfrac{p}{q+x}\\\\\dfrac{1}{y}=\dfrac{1}{\frac{p}{q+x}}=\dfrac{q+x}{p}$

We have x and y intercept:

(2, 0) and (0, 3).

Substitute the coordinates of points to the equation:

$(2,\ 0)\\\\0=\dfrac{q+2}{p}\to q+2=0\to q=-2\\\\(0,\ 3)\\3=\dfrac{q+0}{p}\to3p=q\to3p=-2\to p=-\dfrac{2}{3}$