write a linear equation to model
the situation. Use unit analysis to check your model.
You borrow $40 from your sister. To repay the loan, you pay her $5 a week.
y = 5x+40
To model this situation with a linear equation, we need to determine the relationship between the amount borrowed and the number of weeks it takes to repay the loan.
Let's assign:
- x as the number of weeks passed
- y as the amount of money owed (or the remaining debt)
In this situation, you borrowed $40 and repay $5 each week. This means that at the start (x = 0), you owe $40, and with each passing week, your debt decreases by $5.
We can express the linear equation as:
y = 40 - 5x
Now, let's perform unit analysis to validate our model:
The unit of y represents the amount of money owed, which is in dollars ($).
The unit of x represents the number of weeks passed, which has no unit.
The unit of the right-hand side of the equation is dollars ($). Since both sides of the equation have the same unit, our model is consistent with the units of the given situation. Therefore, our model is correct.
Keep in mind that the linear equation assumes that the amount is repaid steadily and continuously without any additional interest or external factors.