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Let’s go through each pair to compare the rates of change.

### Top Left Pair
- **Panel A**: The equation is \( y = \frac{15}{2}x \), so the rate of change (slope) is \( \frac{15}{2} = 7.5 \).
- **Panel B**: Let's calculate the rate of change using the table values. From \( x = 2 \) to \( x = 4 \), \( y \) goes from 12.5 to 25, giving a rate of change \( \frac{25 - 12.5}{4 - 2} = 6.25 \).
- **Comparison**: \( 7.5 \) (A) is greater than \( 6.25 \) (B).
- **Answer**: A has a **greater** rate of change than B.

### Top Right Pair
- **Panel A**: The equation is \( y = 2x + 4 \), so the rate of change (slope) is \( 2 \).
- **Panel B**: The graph shows a line with points (2,6) and (4,8). The rate of change is \( \frac{8 - 6}{4 - 2} = 1 \).
- **Comparison**: \( 2 \) (A) is greater than \( 1 \) (B).
- **Answer**: A has a **greater** rate of change than B.

### Bottom Left Pair
- **Panel A**: The table values are given. From \( x = 0 \) to \( x = 3 \), \( y \) changes from 2 to 2.6, giving a rate of change \( \frac{2.6 - 2}{3 - 0} = 0.2 \).
- **Panel B**: The graph shows a line with points (2,4) and (6,6). The rate of change is \( \frac{6 - 4}{6 - 2} = 0.5 \).
- **Comparison**: \( 0.2 \) (A) is less than \( 0.5 \) (B).
- **Answer**: A has a **smaller** rate of change than B.

### Bottom Right Pair
- **Panel A**: The equation is \( y = 60x + 25 \), so the rate of change (slope) is \( 60 \).
- **Panel B**: Let's calculate the rate of change using the table values. From \( x = 0 \) to \( x = 5 \), \( y \) goes from 50 to 325, giving a rate of change \( \frac{325 - 50}{5 - 0} = 55 \).
- **Comparison**: \( 60 \) (A) is greater than \( 55 \) (B).
- **Answer**: A has a **greater** rate of change than B.

### Summary of Answers:
1. Top Left: A has a **greater** rate of change than B.
2. Top Right: A has a **greater** rate of change than B.
3. Bottom Left: A has a **smaller** rate of change than B.
4. Bottom Right: A has a **greater** rate of change than B.

Would you like further details on any of these comparisons or have any questions?

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#### Related Questions:
1. How do you find the rate of change from a table of values?
2. What does the slope represent in a linear equation?
3. How can you find the rate of change from a graph?
4. How do you interpret the rate of change in real-world scenarios?
5. What happens to the graph of a line if the rate of change increases?

#### Tip:
The rate of change in linear equations is the coefficient of \( x \) in \( y = mx + b \).

Determine which has a greater or smaller rate of change in each pair of linear functions.

Understand how to compare the rate of change between two linear functions using equations, tables, and graphs. This example problem for Grade 8 involves calculating slopes and identifying whether one function has a greater or smaller rate of change than another.

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