Diego started an exercise program in which each week he works out at the gym between 4.5 and 6 hours and walks between 9 and 12 miles.

a. Make a graph to show the number of hours Diego works out at the gym and the number of miles he walks per week.

b. List three possible combinations of working out and walking that meet Diego's goals.

This is a bit trickier to set up as we are given two different units to work with from the outset, time and distance. Well we know that distance (d) is a function of time (t) and rate (r) so we can set up this equation right away:

d = rt

or in terms of time as is suggested by the needs of the problem: t = d/r

We do not know the rate at which he will be walking so we could set that to x, and we do know that distance is restricted by the following inequality: 9 < = d < = 12. You will need to graph two different lines here, one representing when d = 9 and the second when d = 12 and lightly shading the area in between the curves using the following statements: y = 9 / x and y = 12 / x. The other graph is much easier, you'll only need to lines: y = 4.5 and y = 6 and shade the area in between those.

To be honest, I'm not entirely sure number 1 is worded correctly as the graphs will be tough to construct, especially compared to the relative ease of number 2. You may want to ask your teacher on that one.