the scatter plot and line of best fit below show the length of 10 peoples femur (the long leg bone in the…
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 231 cm?
Answer
Explanation:
Step1: Find the slope of the line
The line passes through points $(30,133)$ and $(63,210)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{210 - 133}{63 - 30}=\frac{77}{33}=\frac{7}{3}$.
Step2: Find the y - intercept of the line
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(30,133)$ and $m = \frac{7}{3}$, we have $y-133=\frac{7}{3}(x - 30)$. Expanding gives $y-133=\frac{7}{3}x-70$. Then $y=\frac{7}{3}x + 63$.
Step3: Predict the femur length
We want to find $x$ when $y = 231$. Substitute $y = 231$ into $y=\frac{7}{3}x + 63$. So $231=\frac{7}{3}x+63$. First, subtract 63 from both sides: $231 - 63=\frac{7}{3}x$, which gives $168=\frac{7}{3}x$. Then multiply both sides by $\frac{3}{7}$ to solve for $x$: $x=\frac{168\times3}{7}=72$.
Answer:
72