Question

Brenna is taking a trip on a train to visit her cousins. The function y = -60x + 220 represents the number of miles to Brenna's destination, y, depending on how many hours she has been on the train, x. What is true about the function?

a) It is linear because the rate of change stays the same.
b) It is linear because the rate of change is decreasing.
c) It is nonlinear because the rate of change stays the same.
d) It is nonlinear because the rate of change is decreasing.

Answer 1

The function y = -60x + 220 is a linear function with a constant rate of change, represented by a straight line that slopes downward to the right as hours on the train (x) increase.

Step-by-step explanation:

The function y = -60x + 220 represents the number of miles to Brenna's destination as a function of the number of hours, x, she has been on the train. This is a linear function because it can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = -60 (which is the rate of change), and b = 220. Because the slope is constant and not zero, the rate of change remains the same, and the graph of this function is a straight line that slopes downward to the right as x increases. Hence, the correct answer is (a) It is linear because the rate of change stays the same.