Question

the scatter plot and line of best fit below show the length of 10 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 250 cm? scatter plot with points (30,130), (40,154), (50,178) answer attempt 1 out of 2

Explanation:

Step1: Find the slope of the line

We have two points on the line of best fit: \((30, 130)\) and \((40, 154)\). The slope \(m\) is calculated as \(\frac{y_2 - y_1}{x_2 - x_1}\). So, \(m=\frac{154 - 130}{40 - 30}=\frac{24}{10} = 2.4\).

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((30,130)\) and \(m = 2.4\).
\(y-130=2.4(x - 30)\)
\(y-130=2.4x-72\)
\(y=2.4x + 58\) (Wait, no, let's re - calculate. \(y-130=2.4(x - 30)\) expands to \(y=2.4x-72 + 130=2.4x + 58\)? Wait, no, let's check with the other point \((50,178)\). If \(x = 50\), \(y=2.4\times50+58=120 + 58=178\). Yes, that works.
Now, we want to find \(x\) when \(y = 250\). So we set up the equation \(250=2.4x+58\).

Step3: Solve for \(x\)

Subtract 58 from both sides: \(250 - 58=2.4x\)
\(192=2.4x\)
Divide both sides by 2.4: \(x=\frac{192}{2.4}=80\)

Answer:

80