Question

Which system of equations is represented by the graph?A. y = x + 4 y = x + 4/ x + 2B. y = x - 4 y = x + 4/ x + 2C. y = x + 4 y = x - 4/ x + 2D. y = x - 4 y = x - 4/ x + 2

Answer 1

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:

`\begin{gathered} y=x+4 \\ y=x-4 \end{gathered}`

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:

`\begin{gathered} y=(x+4)/(x+2) \\ or \\ y=(x-4)/(x+2) \end{gathered}`

We graph the two equations to check which one is correct:

In the graph, we show in green

`y=(x+4)/(x+2)`

and in purple, we have the equation

`y=(x-4)/(x+2)`

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:

`y=(x-4)/(x+2)`

Answer: D

`\begin{gathered} y=x-4 \\ y=(x-4)/(x+2) \end{gathered}`