To determine the equation based on the points given on the graph, we can analyze the information provided.
The points you provided are:
- (2, 30)
- (4, 40)
From these points, we can deduce that the x-values represent the hours rented (the time), and the y-values represent the total cost.
To find the hourly fee and the deposit, we can establish the equation of a line in the form: \[ y = mx + b \] where:
- \( y \) is the total cost,
- \( m \) is the hourly fee,
- \( x \) is the number of hours rented,
- \( b \) is the deposit.
Using the two points, we can first calculate the slope \( m \) (which represents the hourly fee):
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Calculate the change in \( y \) (total cost) and the change in \( x \) (hours):
- From point (2, 30) to (4, 40):
- Change in \( y = 40 - 30 = 10 \)
- Change in \( x = 4 - 2 = 2 \)
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Calculate the slope \( m \):
- \( m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{10}{2} = 5 \)
- So, the hourly fee is \( $5 \) per hour.
Now, to find the deposit \( b \), we can use one of the points. Let's use (2, 30):
- Substitute into the equation \( y = mx + b \):
- \( 30 = 5(2) + b \)
- \( 30 = 10 + b \)
- \( b = 30 - 10 = 20 \)
Thus, the deposit is \( $20 \).
Putting it all together, the total cost equation is: \[ y = 5x + 20 \]
To summarize:
- Hourly fee (\( m \)) = 5
- Deposit (\( b \)) = 20
So, the values to complete the equation for this situation are: Hourly fee = 5, Deposit = 20.
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