https://file.aiquickdraw.com/mathbot/file/1729631715738pakb86ee.jpg

The task asks to write equations in slope-intercept form for two scenarios.

The slope-intercept form of a linear equation is:

\[
y = mx + b
\]

Where:
- $ y $ is the total cost,
- $ x $ is the number of hours,
- $ m $ is the rate per hour (slope), and
- $ b $ is the fixed cost (y-intercept).

### 1. Bicycle rental:
You rent a bicycle for a base fee of $20, plus $2 per hour.

Here:
- The fixed cost ($b$) is $20.
- The hourly rate ($m$) is $2.

Thus, the equation is:
\[
y = 2x + 20
\]
Where:
- $ y $ is the total cost,
- $ x $ is the number of hours.

### 2. Auto repair shop:
The shop charges a base fee of $50, plus $25 per hour.

Here:
- The fixed cost ($b$) is $50.
- The hourly rate ($m$) is $25.

Thus, the equation is:
\[
y = 25x + 50
\]
Where:
- $ y $ is the total cost,
- $ x $ is the number of hours.

Would you like more details on any part of this? Here are some related questions:

1. How do we interpret the slope in a real-world situation?
2. What would change in the equations if the base cost were higher?
3. How would the graph of these equations look?
4. What happens to the total cost if no hours are used?
5. Can these equations be used to find the number of hours for a given total cost?

**Tip:** The slope $m$ in these equations represents the rate of change, or how much the total cost increases with each additional hour.

Write an equation, in slope-intercept form, to model each situation.
1. You rent a bicycle for $20 plus $2 per hour.
2. An auto repair shop charges $50 plus $25 per hour.

Learn how to write linear equations in slope-intercept form to model real-world situations, such as renting a bicycle for $20 plus $2 per hour, or paying an auto repair shop $50 plus $25 per hour. This problem covers key algebra concepts and is suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation