📊 Part 1: Understanding Rate of Change

1. Look at the two walkers below. Circle who walks faster.

Walker A: Walks 1 mile in 10 minutes

Walker B: Walks 1 mile in 20 minutes

Walker A

Walker B

2. Rate of change means:

How much y changes when x increases by 1

How fast you can run

The total distance traveled

3. Look at these two function tables. Circle which function changes faster.

Function A: When x increases by 1, y increases by 3

Function B: When x increases by 1, y increases by 5

Function A

Function B

They change at the same rate

📈 Part 2: Comparing Functions from Different Representations

4. Compare these two functions. Function C has the equation y = 4x + 2. Function D increases by 6 each time x increases by 1. Which changes faster?

Function C (y = 4x + 2)

Function D (increases by 6)

They change at the same rate

5. When comparing graphs, a steeper line means:

The function changes slower

The function changes faster

The function never changes

6. Complete this sentence: "Function ___ changes faster because _______________."

✏️ Part 3: Explain Your Thinking

7. Look at this table for Function E:

x: 1, 2, 3, 4

y: 5, 8, 11, 14

What is the rate of change for Function E? ___________

8. If Function F has the equation y = 2x + 1, and Function E is from question 7, which function changes faster? Explain your reasoning.

9. Create your own real-world example of two things that change at different rates (like the walkers in question 1).

10. Challenge: If you see the equation y = mx + b, what part tells you how fast the function changes? Circle the correct letter and explain why.

m

x

b

Comparing Function Rates

Comparing Function Rates

📊 Part 1: Understanding Rate of Change

📈 Part 2: Comparing Functions from Different Representations

✏️ Part 3: Explain Your Thinking

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