Question

graph
`y \ \textgreater \ (5)/(3) x - 6`Then determine which answer choice matches the graph you drew.

Answer 1

Step-by-step 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.

`y=(5)/(3)x-6`

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.

`\begin{gathered} x=0 \\ y=(5)/(3)x-6 \\ y=(5)/(3)(0)-6 \\ y=0-6 \\ y=-6 \\ \text{ Then, the line passes through the point \lparen0,-6\rparen} \end{gathered}`
`\begin{gathered} x=3 \\ y=(5)/(3)x-6 \\ y=(5)/(3)(3)-6 \\ y=5-6 \\ y=-1 \\ \text{ Then, the line passes through the point \lparen3,-1\rparen} \end{gathered}`

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.