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?
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 given options represent linear models where \( g(x) \) is the predicted grade, and \( x \) represents the number of missed classes. These equations are in the form of:

\[
g(x) = mx + b
\]

where:
- \( m \) (the slope) represents the rate at which grades decrease as students miss more classes.
- \( b \) (the y-intercept) represents the predicted grade when \( x = 0 \), meaning when no classes are missed.

To determine which function will make the **best predictions**, we focus on the slope \( m \) and the intercept \( b \):

1. **Steeper negative slope** (\( m \)) means grades drop more quickly as students miss more classes. A larger negative value indicates a more drastic impact of absences.
2. **Higher intercept** (\( b \)) indicates that students who don’t miss any classes will start with a higher predicted grade.

Now, comparing the options:
- **A. \( g(x) = -2.8x + 93 \)**: A moderate drop in grades with a starting grade of 93.
- **B. \( g(x) = -3.5x + 97 \)**: A steeper drop in grades with a higher starting grade of 97.
- **C. \( g(x) = -3.7x + 98 \)**: An even steeper drop in grades and an even higher starting grade of 98.
- **D. \( g(x) = -4.2x + 101 \)**: The steepest drop in grades but the highest starting grade of 101.

**Option D** gives the highest starting grade, \( 101 \), and assumes the most significant impact for missed classes (steepest slope, \( -4.2 \)). If absences have a significant effect on grades in Mr. Washington's class, this model might best represent that.

Therefore, **the best model is most likely option D: \( g(x) = -4.2x + 101 \)**. 

Would you like to explore the effect of absences on grades further or have any specific questions about linear models?

Here are some related questions:
1. How does the slope of a linear function affect predictions?
2. Why is the intercept important in a linear model?
3. How would predictions change if the slope was less steep?
4. Can a linear model always accurately predict real-world behavior?
5. How would the model change if students' grades didn't decrease consistently?

**Tip:** Always check if the rate of change (slope) aligns with real-world expectations when using linear models!

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?
A.g(x)=−2.8x+93
B.g(x)=−3.5x+97
C.g(x)=−3.7x+98
D.g(x)=−4.2x+101

Learn how to select the best linear model for predicting student grades based on class absences. This problem explores key concepts in linear functions, slope-intercept form, and the effect of absences on student performance. Ideal for students in Grades 9-12.

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