Question

graph this inequality:
$y > -\frac{1}{3}x + 2$
plot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Explanation:

Step1: Identify boundary line

The boundary is $y = -\frac{1}{3}x + 2$, a dotted line (since $>$ is used, no equality).

Step2: Find y-intercept

When $x=0$, $y = -\frac{1}{3}(0)+2=2$. Point: $(0, 2)$

Step3: Find x-intercept

When $y=0$, $0 = -\frac{1}{3}x + 2$
$\frac{1}{3}x=2$
$x=6$. Point: $(6, 0)$

Step4: Test a point for shading

Use $(0,0)$: $0 > -\frac{1}{3}(0)+2$ → $0>2$ (false). Shade opposite region (above the line).

Answer:

1. Draw a dotted line connecting the points $(0, 2)$ and $(6, 0)$.
2. Shade the entire region above this dotted line.