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To create the best linear model based on the provided data set (absences and grades), we can follow these steps:

### Step 1: Organize the Data
The data set provided in the table consists of the following values:

| Absences \(x\) | Grade \(y\) |
|----------------|-------------|
| 2              | 88          |
| 1              | 100         |
| 3              | 91          |
| 5              | 82          |
| 9              | 55          |
| 4              | 82          |
| 7              | 71          |
| 3              | 98          |
| 10             | 68          |
| 7              | 63          |
| 2              | 100         |
| 4              | 92          |
| 5              | 81          |
| 3              | 87          |
| 8              | 81          |
| 0              | 96          |
| 1              | 88          |
| 5              | 59          |
| 2              | 95          |

### Step 2: Find the Linear Regression Equation
We will compute the linear regression equation \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

This equation will give us the best fit line that models the relationship between absences and grades.

Let me calculate the slope and y-intercept based on the data provided.The best-fit linear model based on the provided data is:

\[
g(x) = -3.94x + 99.80
\]

### Step 3: Compare with Given Options
Now, let's compare this with the given options:

- **A:** \( g(x) = -2.8x + 93 \)
- **B:** \( g(x) = -3.5x + 97 \)
- **C:** \( g(x) = -3.7x + 98 \)
- **D:** \( g(x) = -4.2x + 101 \)

The closest option to our calculated model (\( g(x) = -3.94x + 99.80 \)) is **D**: \( g(x) = -4.2x + 101 \).

Thus, **Option D** is the best match for the linear model.

Would you like more details or have any further questions?

Here are five related questions you might find helpful:
1. What is the importance of the slope in a linear equation?
2. How does the y-intercept affect predictions in a linear model?
3. How can we determine if a linear model fits the data well?
4. What methods can we use to check the accuracy of predictions in regression analysis?
5. How does changing data points impact the slope and intercept in linear regression?

**Tip:** Always visualize the data along with the regression line to better understand the fit!

Which of the following functions represents the linear model that will make the best predictions of Mr. Washington’s students' class grades based on how many classes they have missed?

This problem uses linear regression to predict student grades based on the number of classes they have missed. Given a table of absences and grades, the goal is to find the best linear model from a set of options, providing insight into the relationship between class attendance and academic performance. Suitable for students in Grades 9-12.

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