91Ó°ÊÓ

We are given a linear inequality $y>\frac{5}{2}x-4$

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

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

The given inequality is$y>\frac{5}{2}x-4$

We will first replace the inequality with an equal sign and then graph the boundary line.

Here, since the inequality is $y>\frac{5}{2}x-4$and it does not have any equal sign, the boundary line is dashed.

After replacing the inequality, the equation is $y=\frac{5}{2}x-4$. The graph of this equation is,

Consider a point that is not on the boundary line.

Let us consider, $(5,5)$.

We will substitute this point in the given inequality to check if that point is a solution for the inequality or not.

Here, $x=5,y=5$

$$\begin{gathered} y>\frac{5}{2}x-4 \\ 5>\frac{5}{2}\left(5\right)-4 \\ 5>\frac{25}{2}-4 \\ 5>\frac{25-8}{2} \\ 5>\frac{17}{2} \\ 5>8.5 \end{gathered}$$

which is not true.

Therefore, the point $(5,5)$is not a solution for the inequality$y>\frac{5}{2}x-4$.

In the earlier step, we have seen that the point $(5,5)$is not a solution for the inequality $y>\frac{5}{2}x-4$.

Therefore we will shade the side of the boundary line that is opposite to the side containing the point $(5,5)$.

Therefore the graph is

The graph of the linear inequality $y>\frac{5}{2}x-4$is,