91Ó°ÊÓ

We are given an inequality $y>-3x$.

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

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

The given inequality is $y>-3x$.

We will first replace the inequality sign with an equal sign. Then we will draw the boundary line for the graph $y=-3x$.

Since the given inequality is $>$, the boundary line is dashed.

The graph is,

Let us consider a point that is not on the boundary line. Let us take $(-1,1)$.

Here $x=-1,y=1$

Substituting these values in the given inequality, we have

$$\begin{gathered} y>-3x \\ 1>-3(-1) \\ 1>3 \end{gathered}$$

which is not true.

This implies that the point $(-1,1)$ is not a solution for the given inequality.

Since the point $(-1,1)$is not a solution for the given inequality $y>-3x$, we will shade the side of the boundary line that is opposite to the side containing the point $(-1,1)$.

Therefore the graph is,

The points on the shaded region, except for the points on the boundary line represent the solution for the inequality$y>-3x$.

The graph of the linear inequality $y>-3x$is,