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Let's break down and solve the problems from the assessment in the image.

### Problem 6: Constant of Proportionality in the Shopping Center
The manager estimates that 2,574 people enter the shopping center each weekday during the holiday season. The center is open from 9 A.M. to 10 P.M., which is a total of 13 hours (from 9 AM to 10 PM).

- **Step 1:** Find the constant of proportionality by dividing the total number of people by the total number of hours.
\[
\text{Constant of Proportionality} = \frac{2,574 \text{ people}}{13 \text{ hours}} = 198 \text{ people per hour}
\]

- **Explanation:** The constant represents the number of people entering the shopping center per hour. In this case, it's 198 people per hour.

---

### Problem 7: Glee Club Car Wash (Find $k$ for the Relationship $ y = kx $)
We are given the number of cars washed and the amount of money raised. To find $k$, we use the formula $ y = kx $, where $y$ is the money raised and $x$ is the number of cars washed. From the table:

- For 3 cars, $48 is raised. So:
  \[
  48 = k \times 3 \quad \Rightarrow \quad k = \frac{48}{3} = 16
  \]

Thus, $k = 16$. This means that for each car washed, the Glee Club raises $16.

---

### Problem 8: Proportionality in Peach Jam Graph
From the graph, we can observe that the relationship between the number of jars of peach jam and the pounds of peaches used is linear.

To find $k$, we need two points from the graph. Let's take (0, 0) and (18, 9). The slope (which is $k$) is:
\[
k = \frac{9 \text{ pounds}}{18 \text{ jars}} = \frac{1}{2}
\]

Thus, $k = 0.5$, meaning each jar of peach jam requires 0.5 pounds of peaches.

---

### Problem 9: Solving for $k$ in the Equation $y = kx$
We are given the equation $y = kx$, where $y = 1.2$ and $x = 1.5$. To find $k$, we rearrange the equation:
\[
1.2 = k \times 1.5 \quad \Rightarrow \quad k = \frac{1.2}{1.5} = 0.8
\]

So, $k = 0.8$.

---

Would you like more details on any of these steps or explanations?

Here are 5 related questions you could explore:
1. How would the constant of proportionality change if the shopping center was open for fewer hours?
2. What if the Glee Club raised $200 for 12 cars? How would you find $k$?
3. How could you use the equation $y = kx$ to predict the number of cars washed if $400 is raised?
4. What is the interpretation of $k = 0.5$ in the peach jam graph in practical terms?
5. How would $k$ change in Problem 9 if $y = 2.4$ and $x = 3$?

**Tip:** In any problem involving proportionality, always start by identifying two key values that change together. Then divide one by the other to find the constant $k$.

Assessment questions on proportionality involving a shopping center, car wash, peach jam production, and an equation with y = kx.

Explore problems involving the constant of proportionality in real-world contexts such as a shopping center, a car wash fundraiser, and peach jam production. Learn how to solve proportional relationships using the formula y = kx. Suitable for Grade 7 students.

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