Time (hours) Distance (miles)
2 90
3 135
5 225
6 270
a. Find the constant of proportionality.
b. Use the constant of proportionality to write a unit rate for the data in the table.
c. Write an equation to represent the relationship between time, t, and distance, d.
a. To find the constant of proportionality, we need to divide the distance by the time for each set of data and then find the average:
Average rate = (90/2 + 135/3 + 225/5 + 270/6)/4
= 22.5 + 45 + 45 + 45
= 157.5
Therefore, the constant of proportionality is 157.5.
b. The unit rate is simply the constant of proportionality, which is 157.5 miles per hour.
c. We can write the equation as:
d = 157.5t
where d is the distance in miles and t is the time in hours.