Question

select the correct text in the table.
a small musical ensemble has worked five private parties this year. they recorded the number of hours they worked per party and the earnings from each. the ensemble created the following table from the data. the amount the ensemble charges varies depending on the time of year. they charge a flat fee for party reservations.

number of hours, x	1	2	2.5	3	4

the line of best fit for the data is given by the equation below.
$$y = 66.43x + 88.90$$
choose the correct meaning of the rate of change and y-intercept from each column of the table.

rate of change	y-intercept
the flat fee for party reservations	the fee paid per hour the ensemble plays
the amount the earnings increase for each additional hour the ensemble plays	the amount the earnings increase for each additional hour the ensemble plays

Explanation:

Step1: Recall linear equation form

The linear equation is \( y = mx + b \), where \( m \) is the rate of change (slope) and \( b \) is the y - intercept. In the given equation \( y = 66.43x+88.90 \), \( m = 66.43 \) and \( b = 88.90 \).

Step2: Interpret rate of change (\( m \))

The rate of change \( m \) represents the change in \( y \) (earnings) for a unit change in \( x \) (number of hours). So, \( m = 66.43 \) means the amount the earnings increase for each additional hour the ensemble plays.

Step3: Interpret y - intercept (\( b \))

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \) (when the number of hours worked is 0). Since they charge a flat fee for party reservations, when \( x = 0 \) (no hours worked, just reservation), the earnings would be the flat fee. So, \( b = 88.90 \) represents the flat fee for party reservations.

Answer:

Rate of Change: The amount the earnings increase for each additional hour the ensemble plays
y - intercept: The flat fee for party reservations