Let's analyze the problem step by step.

The graph shows a line that has a negative slope. To find which equation represents the line, we need to consider two things:

1. Slope: The line is slanting downward from left to right, so the slope must be negative.
2. Y-intercept: The point where the line crosses the y-axis appears to be at $y = 3$.

Let's review each option:

• Option (a): $y = -\frac{5}{4}x + 3$

  • The slope is $-\frac{5}{4}$ (negative), and the y-intercept is 3. This matches the graph because the line has a negative slope and crosses the y-axis at 3.

• Option (b): $y = \frac{6}{5}x - 3$

  • The slope is $\frac{6}{5}$ (positive), and the y-intercept is -3. This does not match the graph because the line has a positive slope here and a different y-intercept.

• Option (c): $y = 7x + 3$

  • The slope is $7$ (positive), and the y-intercept is 3. This does not match the graph because the slope is positive.

So, the correct answer is (a).

Would you like more details or have any questions?

Here are 5 related questions you can explore:

1. How do you calculate the slope of a line given two points?
2. What is the general form of a linear equation?
3. How can you find the slope from a graph?
4. How does changing the slope affect the steepness of a line?
5. What is the significance of the y-intercept in real-world applications?

Tip: Remember that a negative slope means the line moves downward from left to right!