Explanation
As we can see in the inequality, the variable y is already on the left and everything else on the right. Then, we can do the following steps to graph the given inequality.
Step 1: We plot the equation associated with the inequality.
[tex]y=\frac{5}{3}x-6[/tex]
For this, we can take two x-values, replace them in the above equation and find their corresponding y-values. For example, we can use the values x = 0 and x = 3.
[tex]\begin{gathered} x=0 \\ y=\frac{5}{3}x-6 \\ y=\frac{5}{3}(0)-6 \\ y=0-6 \\ y=-6 \\ \text{ Then, the line passes through the point \lparen0,-6\rparen} \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ y=\frac{5}{3}x-6 \\ y=\frac{5}{3}(3)-6 \\ y=5-6 \\ y=-1 \\ \text{ Then, the line passes through the point \lparen3,-1\rparen} \end{gathered}[/tex]
Now, we plot and join the found points. Since the inequality has the symbol "greater than" (>), we make a dashed line.
Step 2: We shade above the line because the inequality has the symbol "greater than" (>).
Answer
D.
