Step-by-step explanation:
f(x) = mx + b, where m is the slope and b is the y-intercept
You are given m = 4.44 (lb/in^2) for every 10 ft of descent, but you want f(x) to be a function of the depth in inches, so you must find what m is for every inch of descent.
10 ft *(12 in/ft) = 120 inches
So m = 4.44 every 120 inches of descent, therefore
m = 4.44 / 120 = 0.037 every inch of descent
So f(x) = 0.037x + b
To find b, use the fact that f(0) = 15, thus b = 15
So the equation is f(x) = 0.037x + 15
To find when the pressure is 120, set f(x) = 120 and solve for x
120 = 0.037x + 15
0.037x = 105
x = 105 / 0.037 = 2837.8 inches, which is about 236.5 ft
