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The problem provided involves understanding the relationship between the number of hours studied and the exam score using the linear equation \( y = 2.7x + 67 \), where \( y \) represents the exam score, and \( x \) represents the number of hours studied.

We are asked to complete the following sentence:

**"The y-intercept shows that a student who studies [ ] hours can expect to get a score of [ ] on the exam."**

The y-intercept of a linear equation occurs when \( x = 0 \) (i.e., when no hours are studied). Substituting \( x = 0 \) into the equation:

\[
y = 2.7(0) + 67 = 67
\]

This means that when a student studies 0 hours, they can expect to get a score of 67 on the exam.

Therefore, the correct completion of the sentence is:
- **The y-intercept shows that a student who studies 0 hours can expect to get a score of 67 on the exam.**

Thus, the correct answers are:
- **0 hours** (Option A)
- **67 score** (Option G)

Let me know if you'd like further clarification, or have additional questions!

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Here are five follow-up questions you could consider:
1. How is the slope of the equation \( 2.7x \) interpreted in the context of hours studied and exam scores?
2. What exam score would a student expect if they studied for 10 hours using this model?
3. How would the equation change if a student's score was consistently higher by 5 points for every hour studied?
4. What is the significance of the ordered pairs given in the context of the linear model?
5. How can this linear model help students plan their study schedule to improve their exam scores?

**Tip:** The y-intercept often gives insight into a situation when the independent variable is zero. In this case, it shows the base exam score without any studying.

The ordered pairs show the number of hours a student studied in a week, x, and that student's exam score, y. The equation y = 2.7x + 67 can be used to model the relationship between the number of hours a student studied in a week and their exam scores. Complete the sentence about the relationship between the number of hours studied and the exam score.

Understand how the equation y = 2.7x + 67 models the relationship between study hours and exam scores. Learn how to interpret the y-intercept and predict exam scores when no study time is logged. Suitable for Grades 8-10.

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