https://file.aiquickdraw.com/mathbot/file/17280514838647179ei0d.jpg

Let's analyze the problem step by step using the equation of the line of best fit: $ y = 1.82x + 11.36 $, where:

- $ y $ is the amount of money spent on entertainment (in dollars),
- $ x $ is the number of hours worked.

### Part (a): 
**What is the predicted amount of money spent on entertainment for a student who doesn't work any hours?**

If a student works 0 hours, substitute $ x = 0 $ into the equation:
\[
y = 1.82(0) + 11.36 = 11.36
\]
So, the predicted amount of money spent on entertainment is **$11.36**.

### Part (b):
**For an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment?**

From the equation $ y = 1.82x + 11.36 $, the coefficient of $ x $ is 1.82, which means for every 1 hour increase in work, the amount spent on entertainment increases by **$1.82**.

### Part (c):
**What is the predicted amount of money spent on entertainment for a student who works 8 hours?**

Substitute $ x = 8 $ into the equation:
\[
y = 1.82(8) + 11.36 = 14.56 + 11.36 = 25.92
\]
So, the predicted amount of money spent is **$25.92**.

---

Would you like further details on any part of the solution or explanations? Here are 5 related questions to expand on this:

1. How would the equation change if the base spending amount (intercept) increased?
2. What does the slope of 1.82 represent in real-life terms?
3. If the number of hours worked doubled, how would the entertainment spending change?
4. How could you calculate the total amount spent on entertainment for all 23 students combined?
5. What does the intercept 11.36 signify about a student’s spending habits?

**Tip**: The slope of a line in a linear equation always represents the rate of change between the variables (here, dollars per hour worked).

What is the predicted amount of money spent on entertainment based on the line of best fit?

Learn how to use the line of best fit equation y = 1.82x + 11.36 to predict entertainment spending based on hours worked. Solve parts (a), (b), and (c) with step-by-step solutions for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation