https://file.aiquickdraw.com/mathbot/file/1728664946538rlct3dj9.jpg

The equation given in the problem is $ y = 65.75x + 85 $, where $ y $ is the total cost of renting the apartment, and $ x $ is the number of months. 

This equation is in slope-intercept form $ y = mx + b $, where:
- $ m $ is the slope, which represents the rate of change (cost per month),
- $ b $ is the y-intercept, which represents the initial cost when $ x = 0 $ (one-time fee or initial cost).

### Analyzing the equation:
- The slope $ 65.75 $ represents the monthly charge for renting the apartment. This means each month, an additional $65.75 is added to the total rent.
- The y-intercept $ 85 $ represents the initial cost, which is likely a one-time fee like an application or sign-up fee. This cost does not depend on the number of months rented.

### Correct Answer:
The correct option is **A**: "The slope represents the monthly charge for renting the apartment, and the y-intercept represents the application sign-up fee for the apartment unit."

Would you like further details on the breakdown or clarification?

### Related Questions:
1. How can you find the y-intercept from a linear equation in other scenarios?
2. What would happen to the cost equation if the initial application fee increased to $100?
3. How does the slope in a cost function affect long-term expenses in different rental contracts?
4. Can this equation represent situations other than renting an apartment?
5. If Ms. Dollah stays in the apartment for 12 months, what would be the total cost?

### Tip:
Whenever interpreting a linear equation, always associate the slope with a "rate of change" and the y-intercept with a "starting value" or "initial fee."

The cost to rent the new apartment is given by the equation y = 65.75x + 85, where y is the total cost, in dollars, for a rental for a certain number of months, x. In the equation for the cost of renting the apartment, which statement correctly describes BOTH the slope and the y-intercept?

Explore the slope and y-intercept in the linear equation y = 65.75x + 85, representing apartment rental costs. Learn how the slope represents the monthly rental charge, and the y-intercept reflects the initial application fee. This concept is key for students in Grades 8-10 studying algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation