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# Applications Using Direct Variation

## Using proportions to solve y = kx problems.

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The Cost of College
Teacher Contributed

## Real World Applications – Algebra I

### Topic

What’s the total cost of college?

### Student Exploration

Students will use direct variation to understand the cost of attending a four-year university.

Student will need:

1. Access to internet

The Process:

1. Research a four-year university you would like to attend.
2. On the university’s website, find how much it costs to attend that university each year.
3. Create an equation to represent the total cost of attending the university.
4. If I only wanted to spend a total of \$20,000 on college, how many years would I be able to attend?
5. If I wanted spend six years attending this university, how much would it cost?

### Extension Investigation

1. During a student’s first two years living on campus at a four-year university, what would the constant of proportionality be? Why?
1. Would this be a direct variation relationship? Why or why not?
2. What is the equation associated with this relationship?
3. What is the difference between the equations of the proportional relationship and not proportional?

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