Question

A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallons of water. Write an equation the represents the number of y of gallons of water in the tub after x minutes.

Answer 1

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