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?

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 $y = mx + b$.