Question

16. According to the graph, which of the following is true? *Check ALL that apply.



(2 points)
Responses

Reliable Robert has a steeper rate of change than Lenny's Limos.
Reliable Robert has a steeper rate of change than Lenny's Limos.

Lenny's Limos has a larger slope than Fast and Furious.
Lenny's Limos has a larger slope than Fast and Furious.

Lenny's Limos has a lower initial amount of fixed cost than the other two
Lenny's Limos has a lower initial amount of fixed cost than the other two

Fast and Furious initially has a larger fixed cost than Lenny's Limos; but has a lower rate of change.
Fast and Furious initially has a larger fixed cost than Lenny's Limos; but has a lower rate of change.

All three have the same y-intercept.
All three have the same y-intercept.
Question 2
17. The tables below show the number of jumping jacks completed after a given period of time in seconds.

Kimberly:

Time (seconds) Jumping Jacks
3 17
8 37
12 53
16 69


Katrina:

Time (seconds) Jumping Jacks
2 10
5 25
12 60
20 100
(3 points)
a. Which person is doing more jumping jacks per second?

b. Which person had done more jumping jacks initially before the timer started?

c. Which person shows a proportional relationship?

Question 3
18.

Function A: Function B: Function C: y=x+5

(4 points)
a. Which function has the greatest rate of change (slope)?

b. Which function has the smallest y-intercept?

c. Which function would you want to represent your money earned per hour?

d. Which function would give you the highest initial amount of money?

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Answer 1

Let's break down the questions based on the information provided.

### Question 1: Identifying True Statements from the Graph

To determine the truth of each statement without the actual graph, we rely on understanding the concepts of slope and initial amounts (y-intercepts).

1. **Reliable Robert has a steeper rate of change than Lenny's Limos.**
- If Reliable Robert's line has a steeper slope than Lenny's Limos, this statement is true.

2. **Lenny's Limos has a larger slope than Fast and Furious.**
- If Lenny's Limos line is steeper than Fast and Furious, this statement is true.

3. **Lenny's Limos has a lower initial amount of fixed cost than the other two.**
- This refers to the y-intercept. If Lenny's Limos starts lower on the y-axis compared to both other functions, this statement is true.

4. **Fast and Furious initially has a larger fixed cost than Lenny's Limos; but has a lower rate of change.**
- If Fast and Furious starts higher on the y-axis and has a less steep slope than Lenny's Limos, this statement is true.

5. **All three have the same y-intercept.**
- If the lines cross the y-axis at the same point, this statement is true.

### Question 2: Jumping Jacks Comparison

**a. Which person is doing more jumping jacks per second?**

- Calculate the rate of jumping jacks per second for both:

**Kimberly:**
- Average rate = (Total Jumping Jacks) / (Total Time)
- Jumping jacks completed in each interval:
- (3, 17) -> \( \frac{17}{3} \approx 5.67 \)
- (8, 37) -> \( \frac{37 - 17}{8 - 3} = \frac{20}{5} = 4 \)
- (12, 53) -> \( \frac{53 - 37}{12 - 8} = \frac{16}{4} = 4 \)
- (16, 69) -> \( \frac{69 - 53}{16 - 12} = \frac{16}{4} = 4 \)

Overall average will indicate a decline, but leading with the first section.

**Katrina:**
- Average rate = (Total Jumping Jacks) / (Total Time)
- Jumping jacks completed in each interval:
- (2, 10) -> \( \frac{10}{2} = 5 \)
- (5, 25) -> \( \frac{25 - 10}{5 - 2} = \frac{15}{3} = 5 \)
- (12, 60) -> \( \frac{60 - 25}{12 - 5} = \frac{35}{7} = 5 \)
- (20, 100) -> \( \frac{100 - 60}{20 - 12} = \frac{40}{8} = 5 \)

- Overall, Kimberly's highest rate is \(5.67\), so **Kimberly is doing more jumping jacks per second.**

**b. Which person had done more jumping jacks initially before the timer started?**
- Both start counting from zero, so the answer is neither; both started at \(0\).

**c. Which person shows a proportional relationship?**
- A proportional relationship is characterized by consistent rates of change (slope). If both rates were consistent with respect to their intervals:
- Katrina shows a clear rate maintained at \(5\) throughout (proportional).
- Kimberly does not on average due to decreased rates in later observations.

**Answer: Katrina shows a proportional relationship.**

### Question 3: Comparing Functions

For the functions:
- Function A: Unknown slope and y-intercept values (not provided)
- Function B: Unknown slope and y-intercept values (not provided)
- Function C: \(y = x + 5\) (slope = 1, y-intercept = 5)

Without values for Functions A and B, we rely on common knowledge.

**a. Which function has the greatest rate of change (slope)?**
- Need slopes of A and B to determine. If only Function C is known, **answer pending missing values.**

**b. Which function has the smallest y-intercept?**
- Given that C has a y-intercept of 5, if A and B have values greater than 5, C would be it. **Pending missing values.**

**c. Which function would you want to represent your money earned per hour?**
- This depends on the slope. A higher slope is preferable for more earnings per hour. **Pending missing values.**

**d. Which function would give you the highest initial amount of money?**
- A higher y-intercept means more initial amount. Without additional info on A and B, **pending missing values.**

If A and B had respective values, we could obtain values specific to their context.