91Ó°ÊÓ

The boundary line shown in the graph is,

$y=2x-4$

The line $y=2x-4$is the boundary line.

On one side of the line are the points with $y>2x-4$, and on the other side of the line are the points with $y<2x-4$.

Let's test the point $\left(0,0\right)$and see which inequality describes its position relative to the boundary line.

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

$y>2x-4$or $y<2x-4$

Checking for $y>2x-4$, putting $x=0,y=0$

$$\begin{gathered} y>2x-4 \\ ⇒0>2.0-4 \\ ⇒0>-4 \end{gathered}$$

which is true.

Now, Checking for $y<2x-4$, putting $x=0,y=0$

$$\begin{gathered} y<2x-4 \\ ⇒0<2.0-4 \\ 0<-4 \end{gathered}$$

which is false.

Since, $y>2x-4$is true, the side of the line with $(0,0)$is the solution. The shaded region shows the solution of the inequality $y>2x-4$.

Since the boundary line is graphed with a solid line, the inequality includes the equal sign.

The graph shows the inequality$yâ‰\yen 2x-4$