Math for natural sciences help on water pressure

Question

The pressure P on an object under water is linearly related to the depth D. Measurements show that at a depth of 28 feet, the pressure is 26 Ib/Ft squared

and that at a depth of 55 feet, the pressure is 38 Ib/ft squared

1. find an equation for the pressure P as a function of the depth D.
2. Use the equation to find the pressure P at a depth of 40 feet.

Answer 1

For this question, the problem gave us several very important pieces of information.

1. our equation is linear
2. one point is 28 feet with 26lb/ft of pressure
3. one point is 55 feet with 38 lb/ft of pressure

The formula for a linear equation given two points would be

y-y₁=m * (x-x₁)

where "m" is the slope

The first thing that we would need to do is determine the Y and X values of our points

Y= Dependent Variable = Amount of Pressure

X= Independent Variable = Depth in feet

So, our two points would be (28,26) and (55,38)

Our slope is determined by the change in Y over the change in X

in this case, this would be (38-26)/(55-28) = 12/27 or 0.4444

We can now plug these variables into our equation...

y-y₁=m * (x-x₁)

y-26 = (12/27) * (x-28)

y-26 = (0.444) *(x-28)

y-26 = (0.4444)x - (0.4444)(-28)

y-26 = (0.4444x) -12.5

y= (0.4444)x + 13.5

We can then change the variable to match the ones given in the problem.

"y" would become pressure "P" and "x" would become depth "D"

P=(0.444)D+13.5

Now we can solve the second part of the problem by plugging 40 ft in for D

P=(0.4444)D+13.52

P = (0.4444)40+13.5

P= 17.776+13.5

P= 31.276

P = 31 lb/ft

Formula: P=(0.444)D+13.5

Presure at 40 ft: 31 lb/ft