The rental rate for a hedge trimmer has a one time fee of $20 plus $30 for each day of the rental. The graph shows points representing the total cost of the rental.

Question

Which linear equation, in slope-intercept form, models the total cost of the rental over time?

Responses

y = 20x + 30
y = 20 x + 30

y = 2x + 80
y = 2 x + 80

y = 30x
y = 30 x

y = 20x
y = 20 x

y = 30x + 20
y = 30 x + 20
A function graph of a ray with three points. The horizontal axis is labeled Days in intervals of 1 day. The vertical axis is labeled Total Cost in intervals of 10. The ray starts at 0 comma 20 and passes through 2 comma 80 and 3 comma 110.

Answer 1

To determine the correct linear equation that models the total cost of the hedge trimmer rental, we start by identifying the components of the cost structure given in the problem:

• There is a one-time fee of $20.
• There is an additional $30 charge for each day of rental.

The total cost \( y \) can be expressed as a function of the number of rental days \( x \):

1. The one-time fee contributes $20 to the total cost.
2. The daily rental cost is $30 multiplied by the number of days \( x \).

Thus, the equation for the total cost would be:

\[ y = 30x + 20 \]

This is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope (the cost per day) and \( b \) is the y-intercept (the one-time fee).

Given the provided options, the correct equation that models the total cost over time is:

y = 30x + 20