JAMB 2002 · UME · Q37

Use the graph to find the values of $p$ and $q$ if the shaded region is $px + qy < 4$ .

Worked solution (try it first)

The line through $(-4, 0)$ and $(0, 2)$ has gradient $\frac{2 - 0}{0 - (-4)} = \frac12$ and $y$ -intercept 2, so $y = \frac12x + 2$ .
Multiply by 2 and rearrange: $-x + 2y = 4$ .
The origin is in the shaded region, and $-0 + 2(0) = 0 < 4$ , so the region is $-x + 2y < 4$ .
So $p = -1$ and $q = 2$ , option C.