# Question #9606e

Dec 19, 2016

See the explanation

#### Explanation:

Subtract $2 x$ from both sides

$4 y < - 2 x + 9$

Divide both sides by 4

$y < - \frac{1}{2} x + \frac{9}{4}$

As $y$ is less than it can never actually take on the value of $- \frac{1}{2} x + \frac{9}{4}$ Consequently you plot $- \frac{1}{2} x + \frac{9}{4}$ with a dotted line.

As y is less than; you shade in the area under the plotted line as this is the feasible region within which any solution to the inequality may lie but not actually on the line.

Suppose the we had $y$ greater than. If this had been the case then you would shade in the area above the plotted line.

$\textcolor{b r o w n}{\text{I have shown the plotted lines for both formats of this inequality so}}$$\textcolor{b r o w n}{\text{that you can see they are both the same thing.}}$