1. Water is draining from a tank at a constant rate. After 3 minutes, the tank contains 1557 gallons.

Question

After 10 minutes, the tank contains 1494 gallons.
(a) Find a linear equation that gives the amount of water in the tank, G(x), after x minutes have
elapsed. Write the equation in slope-intercept form. Remember to explain what you are doing
at each step and why you are doing it.
(b) Based on your work in part (a), what is the slope of the linear model? Interpret what it means
in the context of the situation.
(c) Use the linear model you created in part (a) to predict the amount of water in the tank after
half an hour. Remember to explain what you are doing and why.
(d) Find the x-intercept of the linear model and interpret what it means in the context of the
situation. Remember to explain what you are doing and why.
(e) Find the y-intercept of the linear model and interpret what it means in the context of the
situation. Remember to explain what you are doing and why

Answer 1

amount = change/min * time + initial amount
G = r x + Gi
G(3) = 1557
G(10) =1494
so r = (1494-1557) / (10-3) = - 9 = slope in gallons / minute
put a point in to get Gi
1557 = -9 * 3 + Gi
Gi = 1557 + 27 = 1584
so
G = -9 x + 1584

Answer 2

your turn now :)

Answer 3

Your data consists of two ordered pairs (3,1557) and (10,1494)
where x is the number of minutes and y is the number of gallons

slope = (1557-1494)/(3-10) = - 63/7 = - 9

so y = -9x + b, with (3,1557) satisfying that equation
1557 = -9(3) + b
b = 1584

y = -9x + 1584

From the work I have done for you, I am sure you can find the
conclusions and answers for each of the parts of your problem.