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 7 hours, planners noted that 2,500 gallons of distilled water remained in the storage tank. Write a linear equation relating the time in hours x since the production line began and the number of gallons y of distilled water in the storage.

Question

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 7 hours, planners noted that 2,500 gallons of distilled water remained in the storage tank. Write a linear equation relating the time in hours x since the production line began and the number of gallons y of distilled water in the storage.

My answer.

Rate is 300/2=150
(7,2,500)
x^1,y^1

y-y^1=m(x-x^1)
y-2,500=150(x-7)
y-2,500=150x-1050
y-2,500+2,500=150x-1050+2,500
Y= 150x+1450

Is this right because I used the point-slope form to write the equation of the line with the given slope and point.

Answer 1

Yes, your approach and solution are correct. You correctly determined the rate at which distilled water is used (150 gallons per hour) and used the point-slope form to write the linear equation. By substituting the values from the given point (7, 2,500) into the equation, you found that the equation of the line relating the time x and the number of gallons y is y = 150x + 1450. Well done!

I agree