Question

c. explain how to use the answers to the previous questions to graph the solution set to the inequality 2y - 3x < 5.

Explanation:

Step1: Isolate y

First, rewrite the inequality $2y - 3x<5$ as $2y<3x + 5$. Then divide each term by 2 to get $y<\frac{3}{2}x+\frac{5}{2}$.

Step2: Analyze the boundary - line

The boundary - line of the inequality $y<\frac{3}{2}x+\frac{5}{2}$ is $y = \frac{3}{2}x+\frac{5}{2}$, which is a straight line with a slope of $\frac{3}{2}$ and a y - intercept of $\frac{5}{2}$. Since the inequality is $y<\frac{3}{2}x+\frac{5}{2}$, the boundary - line is dashed (because the points on the line are not part of the solution set).

Step3: Determine the shading

To determine which side of the line to shade, we can pick a test point not on the line. The origin $(0,0)$ is a convenient test point. Substitute $x = 0$ and $y = 0$ into the original inequality $2y-3x<5$. We get $2(0)-3(0)=0<5$, which is a true statement. So, we shade the region that contains the origin.

Answer:

The solution set of the inequality $2y - 3x<5$ is the region below the dashed line $y=\frac{3}{2}x+\frac{5}{2}$.