To analyze this problem, let’s go through each statement and verify it based on the graph provided:

1. The slope is negative (Statement A):

   • From the graph, we observe that the line is descending as it moves from left to right, indicating a negative slope. This statement is true.

2. The slope is -6 (Statement B):

   • To determine the slope, we can use the formula $\text{slope} = \frac{\Delta y}{\Delta x}$.
   • From the graph, we can pick two points: (0, 0) and (1, -6).
   • Calculating the slope: $\frac{-6 - 0}{1 - 0} = -6$.
   • This statement is true.

3. The relationship is proportional (Statement C):

   • A relationship is proportional if it goes through the origin and maintains a constant ratio. Since the line passes through (0,0) and has a constant slope, it is a proportional relationship. This statement is true.

4. The y-intercept is -3 (Statement D):

   • The y-intercept is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y = 0$. Therefore, the y-intercept is 0, not -3. This statement is false.

Conclusion:

The three true statements are A, B, and C.

Would you like more details or have any questions?

Here are some additional questions to further your understanding:

1. What is the significance of a negative slope in real-world scenarios?
2. How can we determine if a graph represents a proportional relationship?
3. Why is it important to identify the y-intercept in linear equations?
4. How would the interpretation change if the slope were positive?
5. What are other real-life examples of situations where the slope might be negative?

Tip: When analyzing graphs, always check the slope and y-intercept as they provide key insights into the relationship between variables.