To solve the problem, we need to analyze the graph of the two lines and match their equations with the given choices. Here's how we can proceed:

Step 1: Determine the slopes and y-intercepts from the graph

• First Line: It appears to have a negative slope, passing through points like $(0, 1)$ (y-intercept) and $(2, 0)$. The slope $(m)$ can be calculated as: $m = \frac{\text{rise}}{\text{run}} = \frac{1 - 0}{0 - 2} = -\frac{1}{2}.$ Thus, its equation is $y = -\frac{1}{2}x + 1$, or in standard form: $x - 2y = 2.$

• Second Line: It has a positive slope, passing through points like $(0, -4)$ (y-intercept) and $(-2, -6)$. The slope $(m)$ is: $m = \frac{\text{rise}}{\text{run}} = \frac{-4 - (-6)}{0 - (-2)} = \frac{2}{2} = 1.$ Thus, its equation is $y = x - 4$, or in standard form: $x + y = -4.$

Step 2: Compare equations with the given choices

From the above, the system of equations represented by the graph is:

1. $x - 2y = 2$ (First Line).
2. $x + y = -4$ (Second Line).

Step 3: Match with the choices

The correct selections are:

• $x - 2y = 2$
• $x + y = -4$

Would you like me to elaborate on any of the steps or explain the process further?

Here are 5 related questions for deeper understanding:

1. How do you determine the slope of a line from its graph?
2. What are the different forms of a linear equation (e.g., slope-intercept form vs. standard form)?
3. How can you verify the solution to a system of equations by substitution?
4. What does it mean when two lines intersect at a single point?
5. How can graphing be used to estimate solutions to systems of linear equations?

Tip: When analyzing lines on a graph, always look for clear integer-coordinate points to calculate slope and verify the intercepts!