Question

Anthropologists often try to reconstruct information using partial human remains at burial sites. For instance, after finding a femur (thighbone), they may want to predict how tall an individual was. An equation they use to do this is y= 61.4 + 2.4x,where y is the predicted height and x is the length of the femur, both in centimeters.

a. Identify the y-intercept and slope of the equation. Interpret the slope.
b. A femur found at a particular site has length of 50 cm. What is the predicted height of the person who had that femur?

Answer 1

The slope of the equation represents the rate of change in predicted height for each 1 cm increase in the femur length. The predicted height for a femur length of 50 cm is 181.4 cm.

Step-by-step explanation:

a. Slope: The slope of the equation y = 61.4 + 2.4x is 2.4. The slope represents the rate at which the predicted height changes for every 1 cm increase in the femur length. In this case, for every 1 cm increase in the length of the femur, the predicted height increases by 2.4 cm.

b. Predicted Height: To find the predicted height for a femur length of 50 cm, we substitute x = 50 into the equation y = 61.4 + 2.4x. By solving the equation, we get y = 61.4 + 2.4(50) = 61.4 + 120 = 181.4 cm. Therefore, the predicted height of the person with a 50 cm femur is 181.4 cm.