To solve the problem, we need to find which equation corresponds to the graphical lines in the diagram.

Observing the graph:

• Blue Line: It has a positive slope (it's increasing). The slope appears to be $m = 0.5$, as it rises by 1 unit for every 2 units it runs horizontally.

• Red Line: It is a horizontal line. Its equation is simply $y = 5$, as the red line is at $y = 5$ for all values of $x$.

Next, analyzing the options:

We need to find an equation that represents the intersection of these lines or matches the behavior in the graph.

Looking at the blue line, it can be represented by the equation of a line in the form $y = mx + b$. Based on the slope $m = 0.5$ and the fact that the line crosses the y-axis at $b = 2$, the equation for the blue line is likely:

$y = \frac{1}{2}x + 2$

This line intersects the horizontal line $y = 5$.

To solve for the intersection, set the equations equal to each other:

$\frac{1}{2}x + 2 = 5$

Solving for $x$:

$\frac{1}{2}x = 5 - 2 = 3$ $x = 6$

Thus, the solution to the system is $x = 6$.

Now, check the equations in the provided options. The equation $\frac{1}{2}x + 2 = 5$ matches our calculations.

Conclusion:

The correct equation that matches the diagram is:

$\boxed{\frac{1}{2}x + 2 = 5}$

Do you want further details or have any questions?

Here are some additional questions for practice:

1. How do you determine the slope from a graph?
2. What is the general form of a linear equation?
3. How can you identify the y-intercept from a graph?
4. What steps are involved in solving systems of equations graphically?
5. How does a horizontal line differ in terms of slope and equation form compared to a sloped line?

Tip: When analyzing graphs, always check for slope and y-intercept to find the equation of a line.