Question

A bathtub is draining at a constant rate. After 2 minutes, it holds 35 gallons of water. Four minutes later, it holds 15 gallons of water. Write an equation that represents the number y of gallons of water in the tub after x minutes.

Answer 1

Explanation:

The slope-intercept formula is:

y = m x + b,

or: y = b - m x, since the rate is negative.

For the 1st formula we have: y = 30 and x = 2

For the 2nd formula: y = 12 and x = 5 ( because: 5 = 2 + 3, or : 3 minutes later, which can be confusing )

30 = b - 2 m

12 = b - 5 m

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b = 30 + 2 m

12 = 30 + 2 m - 5 m

3 m = 18

m = 18 : 3 = 6

b = 30 + 2 * 6 = 30 + 12 = 42

Answer:

y = 42 - 6 x