91Ó°ÊÓ

The given linear inequality is $2x-3y<6$.

We have to draw a graph that represents the above inequality.

• If the inequality has $â‰\yen$or $≤$, then the boundary line in the graph is a solid line.
• If the inequality has$>$or$<$, then the boundary line in the graph is dashed.

The given linear inequality is$2x-3y<6$.

We will first replace the sign $<$with an equal sign and draw a boundary line for the graph $2x-3y<6$. Since the inequality is $<$, the boundary line will be dashed.

After replacing the inequality sign by an equal sign, the equation is$2x-3y=6$

The graph is,

Consider a point that is not on the boundary line, say $(5,-5)$.

We will substitute the values $x=5,y=-5$in the given inequality $2x-3y<6$to check if the point $(5,-5)$is a solution for the inequality $2x-3y<6$or not.

We have,

$$\begin{gathered} 2x-3y<6 \\ 2\left(5\right)-3(-5)<6 \\ 10+15<6 \\ 25<6 \end{gathered}$$

which is not true.

Therefore, the point$(5,-5)$is not a solution for the given linear inequality.

In the earlier step. we have seen that the point $(5,-5)$is not a solution to the inequality $2x-3y<6$.

Thus we will shade the side of the boundary line opposite to the side containing the point $(5,-5)$. Thus, the graph is,

The points in the shaded region except for the points on the boundary line represent the solution for the linear inequality$2x-3y<6$.

The graph of the linear inequality $2x-3y<6$is