use the drawing tool(s) to form the correct answer on the provided graph. graph the solution to the…

Explanation:

Step1: Rewrite the first inequality in slope - intercept form

Starting with $2x−3y < 15$, we subtract $2x$ from both sides: $- 3y<-2x + 15$. Then divide by $-3$ and reverse the inequality sign: $y>\frac{2}{3}x - 5$. The boundary line is $y = \frac{2}{3}x-5$ and it will be a dashed line (since the inequality is $>$).

Step2: Rewrite the second inequality in slope - intercept form

The second inequality $y\leq x + 2$ has a boundary line of $y=x + 2$ which is a solid line (since the inequality is $\leq$).

Step3: Find the test points

For $y>\frac{2}{3}x - 5$, we can use the test - point $(0,0)$. Substituting $x = 0$ and $y = 0$ gives $0>\frac{2}{3}(0)-5$ or $0>-5$ which is true, so we shade the region above the line $y=\frac{2}{3}x - 5$. For $y\leq x + 2$, using the test - point $(0,0)$ gives $0\leq0 + 2$ which is true, so we shade the region below the line $y=x + 2$.

Step4: Identify the solution region

The solution to the system of inequalities is the region that satisfies both inequalities. It is the region that is above the dashed line $y=\frac{2}{3}x - 5$ and below the solid line $y=x + 2$.

To graph:

1. Use the "Dashed Line" tool to draw the line $y=\frac{2}{3}x - 5$. This line has a $y$ - intercept of $-5$ and a slope of $\frac{2}{3}$.
2. Use the "Line" tool to draw the line $y=x + 2$. This line has a $y$ - intercept of $2$ and a slope of $1$.
3. Use the "Shaded Region" tool to shade the region that is above the dashed line $y=\frac{2}{3}x - 5$ and below the solid line $y=x + 2$.

Since this is a graphing problem and we can't actually draw on the provided graph here, the steps above describe how to graph the solution.

Answer:

Follow the steps above to graph the solution region on the provided graph. The solution region is above the dashed line $y=\frac{2}{3}x - 5$ and below the solid line $y=x + 2$.