WAEC 2012 · Paper 2 · Q7

(a)
(i) Using a scale of 2 cm to 1 unit on both axes, draw on the same graph sheet the graphs of $y - \frac{3x}{4} = 3$ and $y + 2x = 6$ . (ii) From your graph, find the coordinates of the point of intersection of the two graphs. (iii) Show, on the graph sheet, the region satisfied by the inequality $y - \frac34x \ge 3$ .
Separate values with commas, e.g. 3, −2
(b)
Given that $x^2 + bx + 18$ is factorised as $(x + 2)(x + c)$ , find the values of $c$ and $b$ .
Separate values with commas, e.g. 3, −2

The two lines; the shaded region is y − ¾x ≥ 3.

Worked solution (try it first)

Read where the lines cross: about $(1.1, 3.8)$ .
(Check by algebra: $\frac34x + 3 = 6 - 2x$ gives $\frac{11}{4}x = 3$ , so $x = \frac{12}{11} \approx 1.1$ and $y = 6 - \frac{24}{11}$
$= \frac{42}{11}$
$\approx 3.8$ .)

$y - \frac34x \ge 3$ is $y \ge \frac34x + 3$ .
Test the origin: $0 - 0 \ge 3$ is false, so the region is the side of the line away from the origin: on and above the line $y = \frac34x + 3$ .
Draw the line solid (it is included) and label the region.