Question

Which of the following graphs shows the solution for the inequalityy+2≤ 1/2(x-2) ?

Answer 1

We have to find the graph that corresponds to the inequality:.

`y+2\leq(1)/(2)(x-2)`

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:

`\begin{gathered} y+2\leq(1)/(2)(x-2) \\ y\leq(1)/(2)x-1-2 \\ y\leq(1)/(2)x-3 \end{gathered}`

This indicates that the solution region includes values of y that are below the line, and this happens for Option D.

Answer: Option D.