Question 160809
You are given two points (12,200) and (21,164)
Find the slope
{{{m = (y[2]-y[1])/(x[2]-x[1])}}}
{{{m = (164- 200)/(21 -12)}}}
{{{m = -36/9 }}}
{{{m = -4}}} million gallons/day

You are asked to express in terms of t, where t is the numbers of days since the beginning of the month. So you want to get a linear equation in the form
{{{y = mt + b}}} you have m, you need b. t is the number of days since the beginning of the month

Let's find the point (1,y), that will give you the amount of water on the first of the month. We need to 'go back up the line' 12 days. If we are losing -4 million gallons a day, and we back up 12 days, that says there were 4*12 or 48 million more gallons in the tank on the first of the month. 

Add 48 to the amount on day 12 to get (48+200) = 248million gallons.

{{{y = -4t + 248}}}
on day 12, t = 12 and you have 200
on day 21, t = 21  and you have 164

Finally you are asked when the pond is emtpy. At that point, y = 0
{{{0 = -4t + 248}}}
{{{-248 = -4t}}}
{{{248/4 = t}}}
{{{62 = t}}}

You have a little over 2 months from day 1