which is the graph of the solution set of -2x + 5y > 15?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, solve $-2x + 5y>15$ for $y$. Add $2x$ to both sides: $5y>2x + 15$. Then divide by 5: $y>\frac{2}{5}x+3$.

Step2: Analyze the boundary line

The boundary line of the inequality $y>\frac{2}{5}x + 3$ is $y=\frac{2}{5}x+3$. Since the inequality is $y>\frac{2}{5}x + 3$ (not $y\geq\frac{2}{5}x+3$), the boundary line is dashed.

Step3: Determine the shaded region

We can use a test - point, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the original inequality $-2x+5y>15$. We get $-2(0)+5(0)=0$, and $0\not>15$. So, the region that does not contain the origin $(0,0)$ is shaded.

The graph with a dashed line having a positive slope of $\frac{2}{5}$ and $y$-intercept of 3 and the region above the line (not containing the origin) is the correct graph.

Answer:

The graph with a dashed line having a positive slope, $y$-intercept of 3 and the region above the line (not containing the origin) is the solution set graph.