Let's analyze the graph and the provided statements.

Observations:

1. The graph represents a straight line, meaning the relationship is linear.
2. The slope of the line (rate of change) can be calculated using two points from the graph. Using the points $(0, 0)$ and $(3, -8)$:
   • Slope = $\frac{\Delta y}{\Delta x} = \frac{-8 - 0}{3 - 0} = \frac{-8}{3}$.
   • So, the rate of change is $-\frac{8}{3}$.
3. The line passes through the origin $(0, 0)$, which makes the relationship proportional.
4. The equation of the line can be written as:
   • $y = \text{slope} \cdot x = -\frac{8}{3}x$.
   • This does not match $y = -3x$.

Correct Statements:

• The relationship is proportional.
• The rate of change is $-\frac{8}{3}$.
• The relationship is linear.

Incorrect Statements:

• The rate of change is $-\frac{3}{2}$: Incorrect.
• The equation of the line is $y = -3x$: Incorrect.

Let me know if you want further details or calculations.

Related Questions:

1. What is the difference between proportional and linear relationships?
2. How do you derive the equation of a line from its graph?
3. Why is the slope negative in this case?
4. What are the conditions for a line to pass through the origin?
5. How can we verify the slope from multiple points on a graph?

Tip:

Always check if the line passes through the origin to confirm if the relationship is proportional.