Question

1. $y > -\frac{2}{3}x + 5$

Explanation:

Step1: Identify boundary line equation

The boundary line is $y = -\frac{2}{3}x + 5$ (dashed, since inequality is $>$).

Step2: Find y-intercept

When $x=0$, $y = -\frac{2}{3}(0) + 5 = 5$. Plot point $(0, 5)$.

Step3: Find x-intercept

When $y=0$, $0 = -\frac{2}{3}x + 5$
$\frac{2}{3}x = 5$
$x = 5 \times \frac{3}{2} = 7.5$. Plot point $(7.5, 0)$.

Step4: Draw dashed boundary line

Connect $(0,5)$ and $(7.5,0)$ with a dashed line.

Step5: Test a point for shading

Test $(0,0)$: $0 > -\frac{2}{3}(0) + 5$ → $0 > 5$ is false. Shade the region above the dashed line.

Answer:

1. Draw a dashed line through points $(0, 5)$ and $(7.5, 0)$ (representing $y = -\frac{2}{3}x + 5$).
2. Shade the entire region that lies above this dashed line.