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Let's walk through the problems shown in the image:

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### 3. Tiana uses the equation $ c = 21h $ to figure out the total amount, $ c $, she should charge a customer for babysitting for $ h $ hours.

#### (a) What is the constant of proportionality? What does it mean?

- The constant of proportionality is the number that relates $ c $ (total cost) and $ h $ (hours worked). In this case, it is 21, which means Tiana charges **$21 per hour** for babysitting.

#### (b) Tiana charges $94.50 for a job. How long did she babysit for? Show your work.

To solve for $ h $:
\[
c = 21h
\]
Substitute $ c = 94.50 $:
\[
94.50 = 21h
\]
Solve for $ h $:
\[
h = \frac{94.50}{21} = 4.5
\]
So, Tiana babysat for **4.5 hours**.

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### 4. The graph shows the proportional relationship between the minutes Oliver spends reading and the number of pages he reads. 

You are asked to pick two points on the line and describe what they mean. Let's say you choose points $ (2, 6) $ and $ (4, 12) $.

- The point $ (2, 6) $ means that in 2 minutes, Oliver reads 6 pages.
- The point $ (4, 12) $ means that in 4 minutes, Oliver reads 12 pages.

These points show a **proportional relationship** between minutes and pages read.

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### 5. The graph models the proportional relationship between pounds of dog food Savanna's dog eats and the number of days.

We need to tell whether each statement is True or False.

#### (a) The point $ (5, 2) $ means that Savanna's dog eats 5 pounds of dog food in 2 days.

- This statement is **False**. The point $ (5, 2) $ would mean that the dog eats 2 pounds of food in 5 days, not 5 pounds in 2 days.

#### (b) The constant of proportionality is 0.4.

- To find the constant of proportionality, we look at the graph. For example, using the point $ (5, 2) $:
\[
\text{Constant} = \frac{2}{5} = 0.4
\]
This statement is **True**.

#### (c) Savanna's dog eats 4 pounds of food in 10 days.

- Using the constant of proportionality (0.4), for 10 days, the dog eats:
\[
0.4 \times 10 = 4
\]
This statement is **True**.

#### (d) The equation $ y = 2x $ represents this relationship.

- The correct equation should be $ y = 0.4x $, not $ y = 2x $, so this statement is **False**.

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Do you need further details or have any questions? 

Here are five related questions to consider:
1. How would the constant of proportionality change if Tiana charged $30 per hour?
2. What is the meaning of a negative constant of proportionality in a different scenario?
3. How can you verify if a relationship is proportional by looking at a table of values?
4. What equation would represent Oliver reading at a rate of 3 pages per minute?
5. How do you determine if two quantities have a proportional relationship using a graph?

**Tip:** The constant of proportionality is a great way to understand how two variables change in relation to each other; the slope of a straight line in a proportional graph represents this constant!

Tiana uses the equation c = 21h to figure out the total amount, c, she should charge a customer for babysitting for h hours. What is the constant of proportionality? What does it mean? Tiana charges $94.50 for a job. How long did she babysit for?

Learn how to determine the constant of proportionality in a babysitting scenario, using the equation c = 21h. This problem involves solving for the time Tiana worked based on total pay and rates, a key concept for Grades 6-8 math students.

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