Find the linear function

Question

Need a linear function that relates pressure with depth when the pressure is 1 at the surface and 4.75 at a depth of 200 feet.

Answer 1

Depth means to be below the surface.  At surface level, the depth is 0 feet. So a depth of 200 feet is -200 feet.

 

Pressure depends on how deep you go. 

 

Let x = depth

Let y = pressure

 

A linear function is usually in the form       y=mx+b   form , where m is slope and b is y-intercept.  We already know two points on this line based on the info.

 

Point 1 = (-200 , 4.75)

Point 2 = (0, 1)

 

 

Find the slope between these points.

 

m = (1 - 4.75) / (0 - (-200))

 

m = -3.75 / 200

 

m = - 0.01875

 

 

So far, the linear function is     y = - 0.01875x + b

 

 

The point (0, 1) tells us that the y-intercept is 1.

 

y = - 0.01875x + 1