QuestionWhat does the slope of the line tell you about the situation?
Including the initial rental fee, the total cost to rent the paddleboard for 5 hours is .
After the initial rental fee, the paddleboard costs an additional every hour.
Lucia rents the paddleboard for 5 hours.
The initial rental fee is .
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Studdy Solution
STEP 1
What is this asking? Simply put, how does the price of the paddleboard change over time? Watch out! Don't mix up the *initial fee* with the *hourly rate*.
STEP 2
1. Define the variables and the relationship between them.
2. Calculate the slope.
3. Interpret the slope.
STEP 3
Let's **define** our variables!
We'll use for the *time* in hours and for the *total cost* in dollars.
We know there's an initial fee, which we'll call , and an hourly rate, which we'll call .
STEP 4
The relationship between these is a linear equation: .
This is because the *total cost* is the *hourly rate* times the *number of hours*, plus the *initial fee*.
Makes sense, right?
STEP 5
We're given that the *initial fee* is , and the *hourly rate* is .
So our equation becomes .
STEP 6
The **slope** of a linear equation in the form is simply .
In our case, is the *hourly rate*, which is .
STEP 7
The **slope** represents the *rate of change* of the *total cost* with respect to *time*.
In simpler terms, it tells us how much the *total cost* changes for each additional hour of rental.
STEP 8
In this case, the slope is .
This means that for every additional hour Lucia rents the paddleboard, the *total cost* increases by .
So, the slope is the *hourly rate*!
STEP 9
The slope of the line, which is , tells us that the cost of renting the paddleboard increases by for each additional hour of rental.
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