Question

1 which variable is the independent variable in the example? which is the dependent variable? explain how you know.

example
the total cost of renting a tent is equal to a rental fee plus a cleaning fee of $10. write an equation with two variables that shows how to find the total cost of renting a tent based on the rental fee.
you can define variables and use them to write an equation that represents the relationship between the rental fee and the total cost.
r = rental fee in dollars
t = total cost in dollars
the total cost is equal to the rental fee plus $10.
t = r + 10
the equation t = r + 10 can be used to find the total cost of renting a tent.

Explanation:

In the equation \( t = r + 10 \), the independent variable is \( r \) (rental fee) because it can vary freely, and the dependent variable is \( t \) (total cost) because its value depends on the value of \( r \) (when \( r \) changes, \( t \) changes according to the equation). We know this by the definition of independent and dependent variables: the independent variable is the one that is manipulated or can change on its own, and the dependent variable is the one that responds to changes in the independent variable.

Answer:

Independent variable: \( r \) (rental fee in dollars); Dependent variable: \( t \) (total cost in dollars). The independent variable is \( r \) as it can take different values freely, and \( t \) depends on \( r \) (since \( t = r + 10 \), \( t \) changes when \( r \) changes).