Question

The graph below is the solution for which set of inequalities?2+y552+y<420I - 2y <4z+y<5203x - y < 122x + y < 102023 - y<82+y<520320y>0y > 0Y>0Done

Answer 1

`\begin{gathered} 2x-y\leq8 \\ x+y\leq5 \\ x\ge0 \\ y\ge0 \end{gathered}`

Explanation:

To determine the inequalities that represent the graph, we need to find the equations for the lines on the graph.

The line is represented by the following equation:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Therefore, if the line goes down, has a y-intercept of 5, we can calculate the slope with change in y over change in x:

`\begin{gathered} m=(0-5)/(5-0) \\ m=-1 \end{gathered}`

The equation of the line is:

`\begin{gathered} y=-x+5 \\ \text{ Since the shaded region is below the line:} \\ x+y\leq5 \end{gathered}`

The shaded region also has limits with x=0 and y=0, then:

`\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}`

For the other line, which has a y-intercept of -8 and rate of change (slope):

`\begin{gathered} m=(6-0)/(7-4) \\ m=2 \end{gathered}`

Its equation would be:

`\begin{gathered} y=2x-8 \\ \text{ Since the shaded region is on the left:} \\ 2x-y\leq8 \end{gathered}`