Let's analyze the table and answer both parts:

Part A:

The relationship between the two quantities (x and y) can be checked for linearity. To determine if it is linear, we calculate the rate of change (slope) between consecutive points:
The slope formula is:
$\text{slope} = \frac{\Delta y}{\Delta x}$

From the table:

1. Between $x = 1$ and $x = 2$:
   $\text{slope} = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2$

2. Between $x = 2$ and $x = 3$:
   $\text{slope} = \frac{9 - 7}{3 - 2} = \frac{2}{1} = 2$

3. Between $x = 3$ and $x = 4$:
   $\text{slope} = \frac{11 - 9}{4 - 3} = \frac{2}{1} = 2$

Since the slope is constant ($2$) for all intervals, the relationship is linear.

Part B:

The constant rate of change is the slope of the line, which we calculated as:
$\text{Constant rate of change} = 2$

Final Answers:

• Part A: Yes, the relationship is linear.
• Part B: The constant rate of change is $2$.

Let me know if you need further clarification or details!

Related Questions:

1. How do you determine if a relationship is non-linear?
2. What does the constant rate of change represent in real-world situations?
3. If the slope was $3$, how would the table values change?
4. What is the equation of the line that models this relationship?
5. How can you plot these points on a graph to confirm linearity?

Tip:

To confirm linearity, always check the rate of change (slope) between all consecutive points!