Kyle participated in a 63-mile bikeathon. The table shows Kyle’s times at the beginning and end of the bikeathon. Time (hours) Distance Biked (miles) 0 0 4.5 63 Calculate Kyle’s average biking speed in miles per hour. Define variables for the time and distance Kyle biked. Write an equation that represents this situation.

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the time in hours

y ---> the distance biked in miles

we have the points

(0,0) and (4.5,63)

This problem represent a proportional relationship because is a line that passes through the origin

Find the constant of proportionality k

[tex]k=y/x[/tex]

For the point (4.5,63)

[tex]k=63/4.5=14[/tex]

The constant of proportionality or slope represent the average biking speed in miles per hour

so

[tex]k=14\frac{miles}{hour}[/tex]

The equation is equal to

[tex]y=14x[/tex]