Question

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
Earnings,y: 165.50 211.65 245.25 292.45 360.00

The line of best fit for the data is given by the equation below.

Choose the correct meaning of the rate of change and y-intercept from each column of the table.

RATE OF CHANGE
The increase in minutes the ensemble
plays per dollar earned

The flat fee for party reservations

The amount the earnings increase for
each additional hour the ensemble plays

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

Answer 1

Rate of change is the change in earnings per additional unit of time, so the 3rd choice is the best: The amount the earnings increase for each additional hour the ensemble plays.
The y-intercept is the 1st choice: the flat fee for party reservations, since this is constant for all events, no matter how long the event lasts.