A level sensor inputs a range from 450 to 106 ft and outputs

A level sensor inputs a range from 4.50 to 10.6 ft and outputs a pressure from 4 to 16 psi. Find an equation in the form P = mL+b, where P represents Pressure, L represents Level, \"m\" represents the slope on a P vs L graph, and \"b\" represents the P-intercept on a P vs L graph.

Solution

Lets start,

We have to write an equation between the Pressure (P) and Level Sensor Input (L), so taking P on Y axis and L on x axis on a Cartesian Plane.

We have, y₁=4 and y₂=16

and x₁=4.5 and x₂=10.6 now using the Standard way to Find the Equation of Line when we have 2 points

Formula:- (y-y₁)=[(y₂-y₁)/(x₂-x₁)](x-x₁)

Substituting values of the Given variables we get:-

y=1.96x-4.45

Where y is the Pressure (P) and x is the Level Sensor Input (L), so replacing x and y with L and P respectively, we Get

P=1.96L-4.45 Where m=1.96 (Slope of the Equation).

Thank You