Question

leg bone in the thigh) and their height in centimeters. based on the line of best fit, what would be the predicted femur length for someone with a height of 187 cm?

Explanation:

Step1: Find the slope of the line

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(30,127)\) and \((x_2,y_2)=(35,139)\).

$$ m=\frac{139 - 127}{35 - 30}=\frac{12}{5} = 2.4 $$

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((30,127)\) and \(m = 2.4\):

$$ y-127=2.4(x - 30) $$

$$ y-127=2.4x-72 $$

$$ y = 2.4x+55 $$

Step3: Predict the femur length

We want to find \(x\) when \(y = 187\). Substitute \(y = 187\) into the equation \(y = 2.4x+55\):

$$ 187=2.4x+55 $$

$$ 2.4x=187 - 55 $$

$$ 2.4x=132 $$

$$ x=\frac{132}{2.4}=55 $$

Answer:

\(55\) centimeters