Question

question
theres a roughly linear relationship between the length of someones femur (the long leg - bone in your thigh) and their expected height, as expressed in the graph below. what does the slope of
the line represent?
answer
the expected height for someone with a femur length of 55 centimeters.
the change in expected height for every one additional centimeter of femur
length.
the femur length for someone with an expected height of 55 centimeters.
the change in expected femur length for every one additional centimeter of
height.

Explanation:

Step1: Recall the concept of slope in a linear relationship

In a linear relationship \(y = mx + b\) (where \(y\) is the dependent variable, \(x\) is the independent variable, \(m\) is the slope and \(b\) is the y - intercept), the slope \(m=\frac{\Delta y}{\Delta x}\). In the context of a relationship between two variables (here, height \(y\) and femur length \(x\)), the slope represents the change in \(y\) for a unit change in \(x\).

Step2: Interpret the variables

The \(x\) - axis represents femur length (in centimeters) and the \(y\) - axis represents expected height (in centimeters). The slope of the line \(m=\frac{\text{Change in }y}{\text{Change in }x}\). So, the slope of the line representing the relationship between femur length (\(x\)) and expected height (\(y\)) is the change in expected height (\(\Delta y\)) for every one - additional centimeter of femur length (\(\Delta x = 1\)).

Answer:

The change in expected height for every one additional centimeter of femur length.