91Ó°ÊÓ

The given boundary line is $4x-3y=12.$We have to write the inequality shown by the shaded region in the graph with the boundary line.

The line $4x-3y=12$is the boundary line. On one side of the line are the points with $4x-3y>12$and on the other side of the line are the points with $4x-3y<12.$

Let’s test the point $\left(0,0\right),$and see which inequality describes its side of the boundary line.

At $\left(0,0\right),$which inequality is true:

$$\begin{gathered} 4x-3y>12or4x-3y<12 \\ 4\left(0\right)-3\left(0\right)>12or4\left(0\right)-3\left(0\right)<12 \\ 0>12\left[False\right]or0<12\left[True\right] \end{gathered}$$

Since, $4x-3y<12$is true, the side of the line with $\left(0,0\right)$is the solution. The shaded region shows the solution to the inequality $4x-3y<12.$

Since the boundary line is graphed as a dashed line, the inequality does not include an equal sign.

The graph shows the solution to the inequality $4x-3y<12.$