Question

A city's water tank held 12,120 gallons of water at the beginning of the year. Based on monthly data from the reservoir from past years, the equation of the line of best fit for y, the number of gallons of water in the tank, was projected to be y=680x + 12, 120, where x number of months since January 1st. Due to drought conditions, the rate at which water flowed from the reservoir into the tank each month was one-fourth of the projected amount. Identify the transformation required to take the equation y= 680x + 12, 120 to an equation of a line of best fit that models the monthly amount of water in the tank under these drought conditions. State the equation, and describe what its graph looks like in relation to the graph of the projected model.

Answer 1

To model the monthly amount of water in the tank under drought conditions, the equation y = 680x + 12,120 needs to be adjusted. The new equation is y = 170x + 12,120, with a slower increase in water over time.

Step-by-step explanation:

To adapt the equation y = 680x + 12,120 to model the monthly amount of water in the tank under drought conditions, we need to consider that the rate at which water flows into the tank each month is one-fourth of the projected amount. This means that the slope of the new line of best fit will be one-fourth of the slope of the original equation. However, the y-intercept remains the same. Hence, the equation of the line of best fit under drought conditions is y = 170x + 12,120.

The graph of the projected model, y = 680x + 12,120, will have a steeper slope compared to the graph of the line of best fit under drought conditions, y = 170x + 12,120. The new graph will show a slower increase in the amount of water in the tank over time.