Financing a Vehicle: A Lesson on Direct Variation
Description of student activity:
Students will choose three vehicles and prices from internet resources and choose add-ons from a provided table to calculate the total value of each vehicle. These total values will then be used to apply direct variation equations to (1) calculate the days of work required to save enough money to purchase the vehicles and (2) graph a linear financing model. The graphs will also introduce the concepts of vertical transformation, y-intercept, and slope.
To start this activity, students will first research three different vehicle prices online. I have provided a few website suggestions to guide their searches. After finding the initial value of each vehicle, students will then choose add-ons from a provided table to improve the vehicle to their liking. While completing all of this, their choices will be guided by three different budgeting mentalities stated on this handout.
The total cost of each vehicle will then be related to two direct variation functions. The first function will be used to calculate how many days they need to work to save enough for each vehicle. The second function is based on a linear 15-year financing model for each vehicle. The second function for each vehicle will also be graphed on the same coordinate plane so students can see how they compare to one another.
Lastly, students will be introduced to the concept of y-intercept by being asked to explain how each graph would change if a down payment of $10,000 was applied.
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