Problem

Figure 2 shows the points $P$, $Q$ and $R$.

Figure 2

Points $P$ and $Q$ have coordinates $(-1,4)$ and $(4,7)$ respectively.

(a) Find an equation for the straight line passing through points $P$ and $Q$. Give your answer in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.

The point $R$ has coordinates $(p,-3)$, where $p$ is a positive constant.

Given that angle $QPR=90^\circ$,

(b) find the value of $p$.

(Solutions relying on calculator technology are not acceptable.)