Question

the scatter plot and line of best fit below show the length of 10 people’s 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?

Explanation:

Step1: Find slope of best fit line

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Using points $(60,203)$ and $(63,210)$:
$m=\frac{210-203}{63-60}=\frac{7}{3}$

Step2: Write line equation (point-slope)

Use point $(60,203)$:
$y - 203 = \frac{7}{3}(x - 60)$
Simplify to slope-intercept:
$y = \frac{7}{3}x - 140 + 203$
$y = \frac{7}{3}x + 63$

Step3: Rearrange to solve for $x$

We know $y=231$, so:
$231 = \frac{7}{3}x + 63$
Subtract 63: $231-63=\frac{7}{3}x$
$168=\frac{7}{3}x$
Solve for $x$: $x=168\times\frac{3}{7}$

Step4: Calculate final $x$ value

$x=24\times3=72$

Answer:

72 centimeters