Question

the scatter plot and line of best fit below show the length of 12 peoples femur (the long 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 218 cm?

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((60,197)\) and \((63,204)\), we have \(m=\frac{204 - 197}{63 - 60}=\frac{7}{3}\).

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\). Taking the point \((60,197)\), the equation is \(y-197=\frac{7}{3}(x - 60)\). Simplifying gives \(y=\frac{7}{3}x+197 - 140=\frac{7}{3}x + 57\).

Step3: Predict the femur length

We want to find \(x\) when \(y = 218\). Substitute \(y = 218\) into the equation \(218=\frac{7}{3}x+57\). Then \(\frac{7}{3}x=218 - 57 = 161\), and \(x=\frac{161\times3}{7}=69\).

Answer:

\(69\)