Question

Forensic scientists can estimate the overall height of an adult male based on the length of the femur bone. A femur bone that is 18 inches long results in an estimated overall height of 65.85 inches. A femur bone that is 14 inches long results in an estimated overall height of 58.33 inches. Write a linear equation to represent the overall height of an adult male h based on the length of his femur bone f.

Answer 1

h = 1.88f + 32.01

Explanation:

To find the linear equation, we first find the gradient of the linear equation from

(y₂ - y₁)/(x₂ - x₁) = m and using the values of the length of femur and overall height respectively, where x₁ = 18 inches and y₁ = 65.85 inches and x₂ = 14 inches and y₂ = 58.33 inches

So, (y₂ - y₁)/(x₂ - x₁) = m

(58.33 - 65.85)/(14 - 18) = m

-7.52/-4 = m

m = 1.88

So, to find the linear equation, we use

(y - y₁)/(x - x₁) = m where f₁ = 18 inches and h₁ = 65.85 inches

So, (y - y₁)/(x - x₁) = m

(y - 65.85)/(x - 18) = 1.88

(y - 65.85) = 1.88(x - 18)

y - 65.85 = 1.88x - 33.84

collecting like terms, we have

y = 1.88x - 33.84 + 65.85

y = 1.88x + 32.01

Given that y = h = overall height of adult male and x = f = length of femur,

h = 1.88f + 32.01