91影视

The given boundary line is $3x-y=6.$We have to write the inequality shown by the shaded region in the graph with the boundary line.

The line $3x-y=6$is the boundary line. On one side of the line are the points with $3x-y>6$and on the other side of the line are the points with$3x-y<6.$

Let鈥檚 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:

$$\begin{gathered} 3x-y>6or3x-y<6 \\ 3\left(0\right)-0>6or3\left(0\right)-\left(0\right)<6 \\ 0>6\left[False\right]or0<6\left[True\right] \end{gathered}$$

Since, $3x-y<6$is true, the side of the line with $\left(0,0\right)$is the solution. The shaded region shows the solution to the inequality $3x-y<6.$

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 $3x-y<6.$