Question

text description for graph
a. $y>\frac{4}{3}x-2$
b. $y\geq\frac{4}{3}x-2$
c. $y\leq\frac{4}{3}x-2$
d. $y<\frac{4}{3}x-2$

Explanation:

Step1: Find line equation

First, calculate the slope using points $(3,2)$ and $(-3,-6)$:
$$m=\frac{2-(-6)}{3-(-3)}=\frac{8}{6}=\frac{4}{3}$$
Use point-slope form with $(3,2)$:
$$y-2=\frac{4}{3}(x-3)$$
Simplify to slope-intercept form:
$$y=\frac{4}{3}x - 4 + 2=\frac{4}{3}x - 2$$

Step2: Identify line type

The line is dashed, so the inequality uses $<$ or $>$, not $\leq$ or $\geq$.

Step3: Test a point for inequality

Test the origin $(0,0)$ (in the shaded region):
Substitute into $y > \frac{4}{3}x - 2$:
$$0 > 0 - 2 \implies 0 > -2$$
This is true.

Answer:

A. $y>\frac{4}{3}x-2$