SOLUTION: An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo. After the line had run for 9 hours, planners noted that 2,100 gallons of d

Algebra ->  Graphs -> SOLUTION: An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo. After the line had run for 9 hours, planners noted that 2,100 gallons of d      Log On


   

Question 926388: An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo. After the line had run for 9 hours, planners noted that 2,100 gallons of distilled water remained in the storage tank. Write a linear equation relating the time t in hours since the production line began and the number of gallons g of distilled water in the storage tank. Write the equation in slope-intercept form.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That is a rate of 150 gallons per hour, so slope -%28150%29.

y, volume of water in tank
x, time in hours
POINT (9,2100).

Point-Slope form equation for a line will be convenient.
y-v=m%28x-u%29 for any known slope m and known point (u,v).

y-2100=-%28150%29%28x-9%29
y=-%28150%29%28x-9%29%2B2100
y=-150x%2B9%2A150%2B2100
y=-150x%2B1350%2B2100
highlight%28y=-150x%2B3450%29

I changed the variables in my solution so you would really want the solution and result shown as highlight%28g=-150%2At%2B3450%29.
The vertical axis intercept is 3450, meaning so many gallons of water in the storage tank at the beginning, before the operation started.