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Let's work through each of the problems on this page.

### Problem 1: Scatterplot and Line of Best Fit
The scatterplot shows data points and a line of best fit. We need to determine which data point \((x, y)\) has the greatest vertical distance between the y-value of the data point and the y-value predicted by the line of best fit.

#### Steps:
- For each data point, observe the distance between the point and the line of best fit vertically (along the y-axis).
- The point with the largest vertical distance will be the answer.

Let’s estimate:
- \((2, 9.5)\): Line of best fit gives a lower y-value than 9.5.
- \((3, 9)\): The line predicts a much lower y-value here.
- \((6, 7.5)\): Moderate distance.
- \((10, 6)\): This is quite close to the line.

Clearly, \((3, 9)\) has the largest vertical distance from the line of best fit, so the correct answer is:
**Answer: B (3, 9)**

---

### Problem 2: Conversion from Joules to Calories
We need to convert the specific heat of steam from 2.01 joules/gram °C to calories/gram °C using the conversion factor \(1 \text{ joule} = 0.239 \text{ calories}\).

#### Calculation:
\[
2.01 \, \text{joules/gram} \, °C \times 0.239 \, \frac{\text{calories}}{\text{joules}} = 0.48039 \, \text{calories/gram} \, °C
\]

Rounded to the nearest hundredth:
\[
\boxed{0.48 \, \text{calories/gram} \, °C}
\]

**Answer: 0.48 calories/gram °C**

---

### Problem 3: School District Growth Equation
The given equation is \( y = 150x + 8,300 \), where \(x\) represents the number of years after the 2016 school year, and \(y\) represents the total number of students. We need to find how many students will be in the district 1 year after 2016 (i.e., \(x = 1\)).

#### Calculation:
\[
y = 150(1) + 8,300 = 150 + 8,300 = 8,450
\]

**Answer: C (8,450)**

---

### Problem 4: Percent Decrease from 100 to 90
We need to calculate the percentage decrease from 100 to 90.

#### Calculation:
\[
\text{Percent Decrease} = \frac{100 - 90}{100} \times 100 = \frac{10}{100} \times 100 = 10\%
\]

**Answer: A (10%)**

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Let me know if you need any further details or explanations!

Here are 5 related questions:
1. How do you calculate the slope of a line of best fit from a scatterplot?
2. How do you convert units in other scientific contexts, like energy or length?
3. What is the general process for solving a linear equation like the one in Problem 3?
4. What are other ways to calculate percentage increase or decrease in real-life problems?
5. How would you find the rate of growth if the student population increased exponentially instead of linearly?

**Tip:** Always remember to check units when performing conversions or solving physics-based problems to avoid confusion.

Which data point (x, y) has the greatest distance between the y-value of the data point and the y-value predicted by the line of best fit? How do you convert joules to calories? How do you calculate percent decrease from 100 to 90? How many students will there be in a school district based on the given linear equation?

Solve problems involving scatterplots and lines of best fit, unit conversion from joules to calories, linear equations, and percentage decrease. These problems are ideal for students in Grades 9-10.

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