Question

What is the constant of proportionality?

Time (h)
2
3
4
Distance (mi)
80
120
160 a) k=40
b) k=60
c) k=80
d) k=120

Answer 1

The constant of proportionality, k, is found by dividing the distance by time for each pair of given values. In this scenario, k is consistently 40 miles per hour, so the correct answer is (a) k=40.

Step-by-step explanation:

To find the constant of proportionality, k, you need to divide the distance by the time for each of the given pairs of values and see if the result is the same. The constant of proportionality is the consistent rate at which two quantities are related, and in the case of distance and time, it represents speed.

• For 2 hours and 80 miles, divide 80 miles by 2 hours to get 40 miles per hour.
• For 3 hours and 120 miles, divide 120 miles by 3 hours to get 40 miles per hour.
• For 4 hours and 160 miles, divide 160 miles by 4 hours to get 40 miles per hour.

Since all these calculations result in the same number, the constant of proportionality is 40 miles per hour. Therefore, the correct answer is (a) k=40.