Question

a trainer for a professional football team keeps track of the amount of water players consume throughout practice. the trainer observes that the amount of water consumed is a linear function of the temperature on a given day. the trainer finds that when its 90 degrees the players consume about 220 gallons of water and when its 76 degrees the players consume about 178 gallons of water. write a linear function to model the relationship between the gallons of water consumed and the temperature.

Answer 1

treat it as two ordered pairs (t, c) where t is temperature and c is consumption
so we have (90,220) and (76, 178)

slope = (220-178)(/(90-76) = 42/14 = 3

so:
c-220 = 3(t-90)
c = 3t - 270+220

c = 3t - 50

check:
if t = 90, c = 270-50 = 220
if t = 76, c = 228 - 50 = 178