Question

graph the inequality.
$2x + 2y < 18$
a)
b)

Explanation:

Step1: Simplify the inequality

Divide all terms by 2:
$\frac{2x}{2} + \frac{2y}{2} < \frac{18}{2}$
$x + y < 9$
Rearrange to slope-intercept form:
$y < -x + 9$

Step2: Identify boundary line

The boundary is $y = -x + 9$, which has:

• y-intercept: $(0, 9)$
• x-intercept: Set $y=0$, $0 = -x +9 \implies x=9$, so $(9, 0)$

Since the inequality is $<$, the line is dashed.

Step3: Test a point for shading

Use $(0,0)$:
$0 + 0 < 9 \implies 0 < 9$, which is true. So shade the region containing $(0,0)$ (below the line).

Step4: Match to the option

Option A has a dashed line passing through $(0,9)$ and $(9,0)$, with shading below the line, which matches our result.

Answer:

A) [Graph with dashed line through (0,9) and (9,0), shaded below the line]