Begin by drawing the lines for the 3 inequalities.

To draw the lines, treat them as equations and use your knowledge of linear graphs $y = m x + c$ .

The inequalities that are $\leq$ or $\geq$ should be drawn with solid lines and the inequality that is $>$ should be drawn with a dashed line.

For $x \leq 5$ , draw $x = 5$ , a vertical, solid line through 5 on the x-axis.

For $y \leq 4$ , draw $y = 4$ , a horizontal solid line through 4 on the y-axis.

aqa-gcse-graphing-inequalities-m-q4-diagram-1

x = 5 and y = 4 drawn [1]

For $x + y > 6$ , the line with equation $x + y = 6$ needs to be drawn. This is easiest to do by substituting in $x = 0$ and $y = 0$ separately and finding the coordinates where the line crosses the axes.

$\begin{array}{rcl} For x & = & 0 : 0 + y = 6 \Rightarrow y = 6 \\ For y & = & 0 : 6 + 0 = 6 \Rightarrow x = 6 \end{array}$

Plot the points (0, 6) and (6, 0) and join them up. with a dashed line.

z7vumKjp_aqa-gcse-graphing-inequalities-m-q4-diagram-2

y = x drawn [1]

Shade the unwanted regions for each line.

For $x \leq 5$ , the unwanted region is right of the line, so simply shade right of the line $y = 5$ .

For $y \leq 4$ , the unwanted region is above the line, so shade above.

For $x + y > 6$ it is less obvious which side is the wanted or unwanted region, so pick a point with integer coordinates either side of the line and substitute into the inequality to test which side should be shaded.

For example, picking (4, 3),

$\begin{array}{rcl} 2 + 3 & > & 6, false \end{array}$

(2, 3) is in the unwanted region so shade everything on the (2, 3) side of the line $x + y = 6$ .

Finally, don't forget to label the wanted region "R"!

HuXmjgEt_aqa-gcse-graphing-inequalities-m-q4-diagram-3

Correct region clearly indicated [1]

$□$	$x < 1 and y < - 3$
$□$	$x < 1 and y > - 3$
$□$	$x > 1 and y > - 3$
$□$	$x > 1 and y < - 3$

Graphing Inequalities (AQA GCSE Maths)

Exam Questions