Question

which graph best represents the solution set of y + 4 > 1/3x? a b c d

Explanation:

Step1: Rearrange the inequality

First, rewrite $y + 4>\frac{1}{3}x$ as $y>\frac{1}{3}x - 4$.

Step2: Analyze the boundary - line

The boundary - line of the inequality $y>\frac{1}{3}x - 4$ is $y = \frac{1}{3}x - 4$. Since the inequality is $y>\frac{1}{3}x - 4$ (not $y\geq\frac{1}{3}x - 4$), the boundary - line is dashed.

Step3: Find the y - intercept

For the line $y=\frac{1}{3}x - 4$, when $x = 0$, $y=-4$.

Step4: Find the x - intercept

When $y = 0$, we have $0=\frac{1}{3}x - 4$, then $\frac{1}{3}x=4$, and $x = 12$.

Step5: Determine the solution region

We can test a point not on the line, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into $y>\frac{1}{3}x - 4$, we get $0>0 - 4$ which is true. So the region containing the point $(0,0)$ is the solution region.

Answer:

The graph with a dashed line $y=\frac{1}{3}x - 4$ and the region above this line (including the region that contains the origin $(0,0)$) is the correct graph. Without seeing the exact details of each option in a clear - cut way from the provided image, but based on the above analysis, the graph should have a dashed line with a slope of $\frac{1}{3}$ and y - intercept of - 4 and the shaded region above the line.