8. During snowstorms, the city sends out trucks to plow. The amount of snowfall and the number of trucks sent out are shown in the table. PART A Is the relationship between the amount of snowfall and the number of trucks proportional? Explain. $$ \square $$ PART B For a 23 -inch snowfall, how many trucks would the city send out? Explain.

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To assist you effectively with **PART A** and **PART B** of your problem regarding the relationship between snowfall and the number of trucks sent out, I'll outline the general approach you can take. However, to provide specific answers, I would need the data from the table you're referring to. If you can provide the values from the table, I can offer a more detailed response. For now, here's how you can approach each part:

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### **PART A: Determining Proportionality**

**Understanding Proportional Relationships:**
- A relationship between two variables is **proportional** if they increase or decrease at the same rate. Mathematically, this means that the ratio of the two variables remains constant.

**Steps to Determine if the Relationship is Proportional:**
1. **Identify the Pairs:** Look at each pair of values in the table where one value represents the amount of snowfall and the other represents the number of trucks sent out.
   
2. **Calculate the Ratio:** For each pair, divide the number of trucks by the amount of snowfall to find the ratio.

$$
   \text{Ratio} = \frac{\text{Number of Trucks}}{\text{Inches of Snowfall}}
   $$

3. **Compare the Ratios:** If the ratio remains the same for all pairs, the relationship is **proportional**. If the ratio changes, it is **not proportional**.

**Example Illustration:**
Suppose your table looks like this:

| Inches of Snowfall | Number of Trucks Sent Out |
|--------------------|---------------------------|
| 2                  | 4                         |
| 4                  | 8                         |
| 6                  | 12                        |

- Calculate the ratios:
  - $$ \frac{4}{2} = 2 $$
  - $$ \frac{8}{4} = 2 $$
  - $$ \frac{12}{6} = 2 $$

- Since all ratios equal **2**, the relationship is **proportional**.

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### **PART B: Predicting the Number of Trucks for 23 Inches of Snowfall**

Assuming from **PART A** that the relationship is **proportional**, you can predict the number of trucks using the constant ratio found.

**Steps:**
1. **Determine the Constant of Proportionality (k):**
   
   $$
   k = \frac{\text{Number of Trucks}}{\text{Inches of Snowfall}}
   $$

From the example above, $$ k = 2 $$ trucks per inch.

2. **Apply the Proportionality to 23 Inches:**
   
   $$
   \text{Number of Trucks} = k \times \text{Inches of Snowfall} = 2 \times 23 = 46 \text{ trucks}
   $$

**Therefore:**
- For **23 inches** of snowfall, the city would send out **46 trucks**.

**Note:** Ensure you use the actual constant $$ k $$ derived from your table's data for an accurate prediction.

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If you provide the specific data from your table, I can give you a precise answer tailored to your situation!
To determine if the relationship between snowfall and the number of trucks is proportional, compare the ratio of trucks to snowfall for each data pair. If the ratio remains constant, the relationship is proportional. For 23 inches of snowfall, multiply the constant ratio by 23 to find the number of trucks needed.

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