Question

A bathtub is draining at a constant rate. After 2 minutes, it holds 28 gallons of water. Three minutes later, it holds 7 gallons of water. Write an equation that represents the number yy of gallons of water in the tub after xx minutes.

Answer 1

(2,28),(5,7)
slope = (7 - 28) / (5 - 2) = - 21/3 = -7...so it is draining at a rate of 7 gallons per minute

y = mx + b
slope(m) = -7
(2,28)...x = 2 and y = 28
now we sub and find b, the y int
28 = -7(2) + b
28 = -14 + b
28 + 14 = b
42 = b
so ur equation is : y = -7x + 42.....this is basically saying that when full, the bathtub holds 42 gallons and is draining at a rate of 7 gallons per minute

Answer 2

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 = 2For the 2nd formula: y = 12 and x = 5 ( because: 5 = 2 + 3, or : 3 minutes later, which can be confusing  )30 = b - 2 m12 = b - 5 m--------------------b = 30 + 2 m12 = 30 + 2 m - 5 m3 m = 18m = 18 : 3 = 6b = 30 + 2 * 6 = 30 + 12 = 42Answer:y = 42 - 6 x