The temperature of the pool water started at 82 degrees, and it cooling down at 4.0 degrees each hour . If the water temperature is now 78 degrees, then how many hours have passed?

Step-by-step explanation:

Let's set up a coordinate where x is the time at y temperature.  If the water starts out a 82 degrees, the coordinate that represents that is (0, 82).  That says, "before any time has gone by at all, the water was 82 degrees".  That's why we call the time 0...no time has gone by at 0  hours.  If the water is cooling steadily at 4 degrees per hour, that is the value of the rate of change, which is the same as the slope.  If the temp is going down, the slope is -4.  So we have

(0, 82), m = -4

We can use that info to write the linear equation associated with this situation.  I chose the point-slope form, just because:

y - 82 = -4(x - 0) and

y - 82 = -4x + 0 and

y = -4x + 82

That's the linear model.  If we want to know how much time, x, has gone by when the temp is 78, y, then fill in 78 for y and solve for x:

78 = -4x + 82 and

-4 = -4x so

x = 1

One hour has gone by if the temp has dropped from 82 to 78.