Question

the scatter plot and line of best fit below show the length of 14 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 229 cm?
(points on the line: (60,201), (63,208))

Explanation:

Step1: Find the slope of the line of best fit

We have two points on the line: \((60, 201)\) and \((63, 208)\). The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m=\frac{208 - 201}{63 - 60}=\frac{7}{3}\).

Step2: Use the point - slope form to find the equation of the line

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((60, 201)\).
\(y-201=\frac{7}{3}(x - 60)\)
Simplify the equation:
\(y-201=\frac{7}{3}x-140\)
\(y=\frac{7}{3}x + 61\)

Step3: Predict the femur length for height \(y = 229\)

We need to solve for \(x\) when \(y = 229\) in the equation \(y=\frac{7}{3}x + 61\).
Substitute \(y = 229\) into the equation:
\(229=\frac{7}{3}x+61\)
Subtract 61 from both sides:
\(229 - 61=\frac{7}{3}x\)
\(168=\frac{7}{3}x\)
Multiply both sides by \(\frac{3}{7}\):
\(x=\frac{168\times3}{7}=72\)

Answer:

The predicted femur length for a height of 229 cm is 72 centimeters.