Question

Graph the following inequality.Note: To graph the inequality:Select the type of line below (solid or dashed).Plot two points on the line.Click on the side that should be shaded.

Answer 1

Given:

`-4x-y>2`

Consider the line,

`-4x-y=2`

Find the points on the line,

`\begin{gathered} x=0 \\ -4(0)-y=2\Rightarrow y=-2 \\ x=1 \\ -4(1)-y=2\Rightarrow y=-6 \\ x=-1 \\ -4(-1)-y=2\Rightarrow y=2 \end{gathered}`

The graph of the line is,

Now, find the region for inequality.

Consider any point from the right and the left side of the line and check which side satisfies the inequality.

`\begin{gathered} R=(2,0) \\ -4x-y>2 \\ -4(2)-0=-8\text{ >2 is not true.} \end{gathered}`

And,

`\begin{gathered} L=(-2,0) \\ -4x-y>2 \\ -4(-2)-0=8>2\text{ is true} \end{gathered}`

Therefore, the graph of the inequality is,

Note that inequality does not contain boundary points.