# Independent/dependent variable and modeling equations

## Homework Statement

8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of$20 is charged, when the boat is returned.

a. Identify the independent and dependent variables, including units, for this scenario.

b. Write an equation that models this scenario.

c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

## Homework Equations

y = mx + b

3. The Attempt at a Solution

a. Identify the independent and dependent variables, including units, for this scenario.

The Independent variable is the $20 cleaning fee. The dependent variable is$12 per hour. If I wrote this as the formula as a line it would be written as: Y = 12x + 20.
20 would be the initial value and initial value is always the independent variable. While 12 would be the slope, and the slope is always the dependent variable.

b. Write an equation that models this scenario.

a equation that can model this scenario is y = mx + b. Were y is the total cost, m the amount of money per hour ($12). X represents the number of hours and b is the cleaning fee. If we were to put this in equation form it would look like this: Y = 12x + 20 c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario. The marina could offer$14 per hour ($14/hour), which is a higher hourly rate compared to the first marina, and an$11 cleaning fee after the rowboat is returned, which can be considered a lower cleaning fee compared to the cleaning fee offered by the first marina.
So using the equation y = mx + b, where y is the total cost, m is the amount of dollars per hour, x is the total amount of hours, and b is the cleaning fee, we can formulate an equation: y = 14x + 11.

Im pretty sure that my solutions are correct, I just want to be 100% sure.

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## Homework Statement

8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of$20 is charged, when the boat is returned.

a. Identify the independent and dependent variables, including units, for this scenario.

b. Write an equation that models this scenario.

c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

## Homework Equations

y = mx + b

3. The Attempt at a Solution

a. Identify the independent and dependent variables, including units, for this scenario.

The Independent variable is the $20 cleaning fee. The dependent variable is$12 per hour. If I wrote this as the formula as a line it would be written as: Y = 12x + 20.
20 would be the initial value and initial value is always the independent variable. While 12 would be the slope, and the slope is always the dependent variable.
Those are not variables at all. x and y are the variables.

Later on you say that x represents the number of hours a boat is rented and y is the total rental cost.
Which of those is the dependent variable, and which is the independent variable?
b. Write an equation that models this scenario.

a equation that can model this scenario is y = mx + b. Where y is the total cost, m the amount of money per hour ($12). X represents the number of hours and b is the cleaning fee. If we were to put this in equation form it would look like this: Y = 12x + 20 c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario. The marina could offer$14 per hour ($14/hour), which is a higher hourly rate compared to the first marina, and an$11 cleaning fee after the rowboat is returned, which can be considered a lower cleaning fee compared to the cleaning fee offered by the first marina.
So using the equation y = mx + b, where y is the total cost, m is the amount of dollars per hour, x is the total amount of hours, and b is the cleaning fee, we can formulate an equation: y = 14x + 11.

Im pretty sure that my solutions are correct, I just want to be 100% sure.

The independent in this case would be the hours and the dependent would be the total rental cost since the total rental cost depends on how long you rent the boat for. right?

SammyS
Staff Emeritus