Answer
$y=\displaystyle \frac{q}{p}x$
Work Step by Step
If $p\neq 0$, the line is not vertical, so it has slope.
We can write its equation in the form
$y=mx+b,$ (find m and b).
The intercept is $b=0$, since the line passes through (0,0).
Slope:
Given $(x_{1},y_{1})=(0,0)$ and $(x_{2},y_{2})=(p,q)$ on a line, calculate the slope :
$m=\displaystyle \frac{q-0}{p-0}=\frac{q}{p}$
Thus,
$y=\displaystyle \frac{q}{p}x$
