We have to find the graph that corresponds to the inequality:.
[tex]y+2\leq\frac{1}{2}(x-2)[/tex]
We start by stating that the line is included as part of the solution (because of the equal sign) and that is represented by a full line, so we can discard options A and B, which have dashed lines.
The boundary line pass through point (2, -2), given the expression.
Both the remaining options have the same line, so we have to use the sign to differentiate them.
If we rearrange the inequality we have:
[tex]\begin{gathered} y+2\leq\frac{1}{2}(x-2) \\ y\leq\frac{1}{2}x-1-2 \\ y\leq\frac{1}{2}x-3 \end{gathered}[/tex]
This indicates that the solution region includes values of y that are below the line, and this happens for Option D.
Answer: Option D.
