Question

Phil is riding his bike. He rides 23 miles in 2 hours, 34.5 miles in 3 hours, and 46 miles in 4 hours. Find the constant of proportionality and write an equation to describe the situation. Let x represent the number of hours.

Answer 1

The constant of proportionality (known as "speed" in this case) is 12.5 miles per hour. 
d= 12.5 x t 

To find the constant of proportionality, divide one value in each pair by the other. If this relationship is a true direct proportionality , when you repeat these for every pair, your will come up with the same value:

For example

25miles÷2hours=12.5mileshour

A direct proportionality will always result in an equation that resembles this:

y=kx

where y and x are the related quantities and k is the constant of proportionality. If you draw a graph using the values you have, the graph will show a straight line the passes through the origin. The slope of this line will be the constant of proportionality. (And if the values given are real physical quantities, this constant will contain important information about the situation you are studying!)

Answer 2

The equation is 12.5n where n stands for any hour that Phil is riding his bike. I'm using the nth term here though.