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 221 cm?

Explanation:

Step1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(60,200)$ and $(63,207)$, we have $m=\frac{207 - 200}{63 - 60}=\frac{7}{3}$.

Step2: Find the y - intercept of the line

Using the point - slope form of a line $y - y_1=m(x - x_1)$ with the point $(60,200)$ and $m = \frac{7}{3}$, we get $y-200=\frac{7}{3}(x - 60)$. Expanding gives $y-200=\frac{7}{3}x-140$, so $y=\frac{7}{3}x + 60$.

Step3: Predict the femur length

We want to find $x$ when $y = 221$. Substitute $y = 221$ into $y=\frac{7}{3}x+60$. So $221=\frac{7}{3}x + 60$. Subtract 60 from both sides: $221-60=\frac{7}{3}x$, which gives $161=\frac{7}{3}x$. Multiply both sides by $\frac{3}{7}$: $x=\frac{161\times3}{7}=69$.

Answer:

69