Question

A full bathtub is emptying at a

fixed rate. Which of the following
equations may relates the amount
in water y, in gallons, with the
amount of time, x minutes. Assume
the bathtub is holding 100 liters
of water, and empties at a rate of
5.8 liters per minute.

Answer 1

D 5y + 29x = 500

Explanation:

Slope-intercept form of a linear equation: y = mx + b

(where m is the slope/rate of change, and b is the y-intercept)

Given:

• bathtub holds 100 liters

⇒ when x = 0, y = 100

Therefore, b = 100

Given:

• the water is emptying at a rate of 5.8 liters/min

Note that the water is decreasing in volume as time goes by. Therefore, the rate of change is negative, so m = -5.8

Inputting these values into the equation gives:

y = -5.8x + 100

Multiply the equation by 5:

5y = -29x + 500

Rearrange:

5y + 29x = 500

Therefore, D is the solution.