The image displays a graph with two intersecting lines and a set of equation options to match with the graph. Let's identify the correct equations that represent the two lines.

Steps to Solve:

1. Identify the slopes and y-intercepts:

   • The first line has a negative slope, crossing the y-axis at $y = 6$.
   • The second line has a positive slope, passing through the origin $(0, 0)$.

2. Verify with given equations:

   • The first line's equation appears to fit the form $y = mx + b$, where the slope $m$ is negative and $b = 6$.
   • The second line's equation should have a positive slope $m$, passing through $(0, 0)$, meaning $b = 0$.

Testing Options:

• Option A ($y = \frac{5}{4}x$): Has a positive slope ($\frac{5}{4}$), matching the second line.
• Option B ($y = 6 - 2.5x$): Has a slope of $-2.5$ and $y$-intercept $6$, matching the first line.
• Option C ($y = 2.5x + 6$): Slope and intercept do not match either line.
• Option D ($y = 6 - 3x$): Slope is too steep compared to the graph.
• Option E ($y = 0.8x$): Has a positive slope but is too shallow.

Correct Equations:

• $y = \frac{5}{4}x$ (Option A) for the positive-slope line.
• $y = 6 - 2.5x$ (Option B) for the negative-slope line.

Would you like further explanation or additional details?

Here are 5 related questions for deeper understanding:

1. How do you determine the slope of a line from a graph?
2. What is the significance of the $y$-intercept in the equation of a line?
3. How can you verify that a point lies on a given line's equation?
4. What is the difference between parallel and perpendicular lines in terms of slope?
5. How do you find the intersection point of two lines algebraically?

Tip: Always rewrite equations in slope-intercept form ($y = mx + b$) when analyzing graphs.