you rollerblade at an average speed of 8 miles per hour. the number of miles m you rollerblade during h hours is modeled by m=8h. do these two quantities have direct variation?

A direct variation should have a constant positive slope, and zero y-intercept.

For example,
y=4x is a direct variation, but
y=-2x is not (negative slope),
nor
y=2x+100 (non-zero y-intercept).

Yes, these two quantities have direct variation. In mathematics, direct variation is a relationship between two variables where one variable is a constant multiple of the other.

To determine if two quantities have direct variation, you need to check if they can be written in the form y = kx, where y and x are the two variables and k is a constant called the constant of variation.

In this case, "m" represents the number of miles rollerbladed and "h" represents the number of hours spent rollerblading. The equation m = 8h can be rewritten as m = 8 * h. Here, "m" is equal to 8 times "h", which matches the form y = kx, where k (the constant of variation) is 8.

Since m = 8h can be written in the form y = kx, with k = 8, we can conclude that the number of miles rollerbladed (m) and the number of hours spent rollerblading (h) have direct variation.