91Ó°ÊÓ

Given linear inequality is$y≤-5x$

The graph of the linear inequality is to be determined.

When a inequality consists $<,>$a dotted line is used to represent the boundary and when the inequality consists $≤,â‰\yen$solid line is used to represent the boundary line.

Boundary line of an inequality is determined by replacing the inequality sign with equality sign in the given linear equality.

Hence the boundary line is $y=-5x$.

Two points are to be determined the graph the line. Assuming two x values and determining the corresponding y values gives the points.

When $x=0$:

$$\begin{gathered} y=-5x \\ y=-5\left(0\right) \\ y=0 \end{gathered}$$

When $x=1$:

$$\begin{gathered} y=-5x \\ y=-5\left(1\right) \\ y=-5 \end{gathered}$$

Hence the line passes through the points$\left(0,0\right),\left(1,-5\right)$

Since the inequality is $≤$, the boundary line is represented by a solid line.

The region to be shaded for the inequality is determined by checking if a point satisfies the inequality.

Plugging $\left(1,1\right)$in the inequality:

$$\begin{gathered} y≤-5x \\ 1\stackrel{?}{≤}-5\left(1\right) \\ 1≰-5 \end{gathered}$$

The point does not satisfy the inequality, hence the shading is on the other side of the line.

The graph of the linear inequality is