Graph the inequality $0.4x+0.6y\ge 90$where $x$ is midterm score and $y$ is the final term score.

Which Rosa’s professor says that the midterm exam will count for $40\%$of each students grade and final exam will count for means$60\%$

The Consider the inequality showing this situation as

$0.4x+0.6y\ge 90$

Here, the variables are respectively the midterm score and final exam score.

The graph of the above inequality is represented as follows:

The corresponding equation of the inequality is

$0.4x+0.6y\ge 90$

Since, the inequality sign is $\ge$so, the boundary will be solid.

Check the origin point $\left(0,0\right)$

On substituting the value $x=0$and $y=0$in the inequality.

$\begin{array}{l}0.4x+0.6y\ge 90\\ 0.4\left(0\right)+0.6\left(0\right)\ge 90\\ 0\ge 90\end{array}$

The origin does not satisfy the inequality, therefore, the shaded region not containing the origin side.

Therefore, all points lying above the solid boundary satisfies the inequality.

The graph of the inequality

$0.4x+0.6y\ge 90$is represented as the shaded region as follows.