Step 1. We have two equations represented in the graph. One is the red line and the other is the blue graph.
The red line represents a linear equation,
and the blue segments represent a rational equation.
Step 2. For the linear equations, we have only two options given:
[tex]\begin{gathered} y=x+4 \\ y=x-4 \end{gathered}[/tex]
Graphing both lines to pick which one is the line shown in the problem:
The green line is y=x+4,
and the purple line is y=x-4.
Compared with our graph, we have the one that crosses the y-axis at -4, Thus it is the equation y=x-4.
Step 3. For the rational equation, we are given two options to choose from:
[tex]\begin{gathered} y=\frac{x+4}{x+2} \\ or \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]
We graph the two equations to check which one is correct:
In the graph, we show in green
[tex]y=\frac{x+4}{x+2}[/tex]
and in purple, we have the equation
[tex]y=\frac{x-4}{x+2}[/tex]
As you can see, the second one, (the purple one) is the one shown in the graph from this problem, thus, the second equation is:
[tex]y=\frac{x-4}{x+2}[/tex]
Answer: D
[tex]\begin{gathered} y=x-4 \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]
