Question

You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pull the plug, there are 10 gallons left. Assume that the number of gallons varies linearly with the time since the plug was pulled. Write the particular equation expressing the number of gallons (g) left in the tub in terms of the number of seconds (s) since you pulled the plug.

Answer 1

consider your data as ordered pairs of the form
(s,g)
so we have (40,13) and (60,10)

so we could find "slope", in this case number of gallons/second
= (10-13)/(60-40) = -3/20

so g = (-3/20)s + b
using (40,13)
13 = (-3/20)(40) + b
13 = - 6 + b
b = 19

g = (-3/20)s + 19

A good follow-up question would have been:
How long would it take for the tub to empty?