~ 2.5 ~

If Kiran rode his bike at a constant 10 miles per hour, his distance in miles, d, is proportional to the number of hours, t, that he rode. We can write the equation

d = 10t

With this equation, it is easy to find the distance Kiran rode when we know how long it took because we can just multiply the time by 10.

We can rewrite the equation:

This version of the equation tells us that the amount of time he rode is proportional to the distance he traveled, and the constant of proportionality is 110. That form is easier to use when we know his distance and want to find how long it took because we can just multiply the distance by 110.

When two quantities x and y are in a proportional relationship, we can write the equation

y = kx

and say, “y is proportional to x.” In this case, the number k is the corresponding constant of proportionality. We can also write the equation

and say, “x is proportional to y.” In this case, the number (1/k) is the corresponding constant of proportionality. Each one can be useful depending on the information we have and the quantity we are trying to figure out.