How would I be able to determine if one of these is linear and non proportional?
Select the best description of a real world situation where the relationship is linear and non-proportional.
Amanda borrows a flute from a friend for $5 per week and then pays $31 dollars per week for lessons.
Amanda buys a flute for $500 dollars and then pays $31.00 per week for lessons
or
Amanda rents a flute for $50.00 each month and then pays $31.00 per week for lessons.
All of these are linear, here are the equations.
a. Acost=weeks(5+31)
b. Acost=500+31*weeks
c. Acost=weeks(50+31)
all are linear equations, all will plot as lines on a graph of cost vs time.
To determine if a relationship is linear and non-proportional, you can examine the pattern of the values and see if they consistently increase or decrease by the same amount or proportion. Here's how you can analyze each situation:
1. Amanda borrows a flute from a friend for $5 per week and then pays $31 per week for lessons: In this scenario, you can determine if it is a linear relationship by examining whether the total cost increases or decreases at a constant rate. If Amanda's total cost (flute + lessons) remains the same each week, regardless of the number of weeks, the relationship is linear and non-proportional.
2. Amanda buys a flute for $500 and then pays $31 per week for lessons: To determine if this relationship is linear and non-proportional, you need to examine if the total cost (flute + lessons) changes at a constant rate. If Amanda pays the same amount every week for lessons, regardless of the number of weeks, and the cost of the flute is a one-time payment, the relationship is linear and non-proportional.
3. Amanda rents a flute for $50 each month and then pays $31 per week for lessons: Similarly, inspect if the total cost (rental + lessons) increases or decreases at a constant rate. If the rental cost remains the same each month, regardless of the number of months, and Amanda pays the same amount every week for lessons, the relationship is linear and non-proportional.
After analyzing each situation as described above, you can determine which one represents a real-world situation with a linear and non-proportional relationship.