https://r2.erweima.ai/mathbot/image/1726686121275ik451tas.jpg

The problem asks to identify the independent and dependent variables in a given linear relationship, and to calculate the rate of change.

### 1. Identifying Variables
- **Independent variable**: This is the variable that influences the outcome, typically something that is controlled or can be freely adjusted.
- **Dependent variable**: This is the variable that changes in response to the independent variable.

In this case:
- The **independent variable** is the number of students, because the cost of dinner depends on how many students attend.
  - Answer: **D. The number of students**
  
- The **dependent variable** is the cost of dinner, because it changes based on how many students are attending.
  - Answer: **F. The cost of dinner**

### 2. Finding the Rate of Change
The problem provides the following information:
- 5 students have a dinner cost of $70.
- 8 students have a dinner cost of $112.

The rate of change (or slope) in a linear relationship is calculated as:

\[
\text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Number of Students}} = \frac{112 - 70}{8 - 5} = \frac{42}{3} = 14
\]

Thus, the rate of change is **$14 per student**.

Would you like further details on this explanation or have any other questions?

Here are 5 related questions to expand on this topic:
1. How can you graph this linear relationship between students and cost?
2. What does the rate of change tell us in real-life situations?
3. Can you calculate the total cost for 10 students using this rate of change?
4. How would the equation of the line look for this situation?
5. What other examples can you think of that involve a linear relationship like this?

**Tip:** The independent variable is often what you can control, while the dependent variable is what gets affected or measured based on that.

The cost of dinner is $70 for five students and $112 for eight students. State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situation.

In this problem, students learn to identify independent and dependent variables in a linear relationship and calculate the rate of change. The scenario involves the cost of dinner for different numbers of students, with a detailed solution using the slope formula. Suitable for students in 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