Question

The table shows the distance a cyclist rides her bicycle over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?
Bike Riding Distance

Time
(minutes) Distance
Traveled (ft)
1 1120
2 2240
3 3360
4 4480
A. The rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
B. The rate of change is constant and represents a speed of 3360 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
C. The rate of change is constant and represents a speed of 2240 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.
D. The rate of change is constant and represents a speed of 4480 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.

Answer 1

From the relationship between the distance and time, the rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.

What is a linear equation?

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the distance travelled by the bike after x minutes.

From the table:

Rate of change = (4480 - 1120) / (4 - 1) = 1120 ft/min

The rate of change is constant and represents a speed of 1120 ft/min. The cyclist rides her bike at a rate of 1120 ft/min.

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