Daniel's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y, equals, 7, point, 3, x, plus, 55*y*=7.3*x*+55, where y*y* represents the expected quiz score and x*x* represents hours spent on homework that week. What could the number 7.3 represent in the equation?

Answer

Multiple Choice Answers

A student's expected quiz score if they spent 62.3 hours on their homework.

A student's expected quiz score if they spent 1 hour on their homework.

The change in expected quiz score for every additional one hour students spend on their homework.

How many hours a student spends studying all year.

The equation provided is \( y = 7.3x + 55 \), where:

- \( y \) represents the expected quiz score.
- \( x \) represents the number of hours spent on homework that week.
- \( 7.3 \) is the coefficient of \( x \).
- \( 55 \) is the y-intercept, which represents the expected quiz score when no hours are spent on homework.

To understand what \( 7.3 \) represents, let's break it down:

- In a linear equation of the form \( y = mx + b \), \( m \) is the slope of the line.
- The slope (\( m \)) indicates the rate of change in \( y \) with respect to \( x \).
- In this context, \( m = 7.3 \) represents the **change in the expected quiz score** for every additional hour spent on homework.

Therefore, **the number 7.3 represents the change in expected quiz score for every additional one hour students spend on their homework**.

**Correct Multiple Choice Answer:**
- **The change in expected quiz score for every additional one hour students spend on their homework.**

Would you like more details on interpreting linear equations, or do you have any other questions? Here are five related questions:

1. How do you interpret the y-intercept in this context?
2. What would the expected quiz score be if a student spent 3 hours on their homework?
3. How does the slope of a line affect the steepness of the line on a graph?
4. If the coefficient of \( x \) was negative, how would that change the relationship between time spent on homework and quiz scores?
5. Can you use this equation to predict a quiz score if a student spends zero hours on homework?

**Tip:** In any linear equation, the slope tells you how much the dependent variable (in this case, quiz score) changes for each unit change in the independent variable (hours spent on homework).

Explore the relationship between the time spent on homework and quiz scores through a linear equation. Learn how the coefficient affects the expected quiz score and interpret the y-intercept. Suitable for Grades 7-9.

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