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 femur length for someone with an expected
height of 57 centimeters.
the change in expected femur length for every one
additional centimeter of height.
the expected height for someone with a femur length
of 5.5 centimeters.
the change in expected height for every one
additional centimeter of femur length.

Explanation:

Step1: Recall the concept of slope in a linear relationship

The slope \(m\) of a line in the context of a linear relationship \(y = mx + b\) (where \(y\) is the dependent variable and \(x\) is the independent variable) represents the rate of change of \(y\) with respect to \(x\). In a graph of height (\(y\)-axis) versus femur length (\(x\)-axis), the slope formula is \(m=\frac{\Delta y}{\Delta x}\), which means the change in \(y\) (height) for a unit - change in \(x\) (femur length).

Step2: Analyze the options based on the slope concept

• If we consider the slope as the change in height (expected height) for a change in femur length:
• The formula for slope \(m=\frac{\text{Change in }y}{\text{Change in }x}\). Here, \(y\) is the expected height and \(x\) is the femur length.
• The slope of the line in the context of this graph (where \(y\) - axis is expected height and \(x\) - axis is femur length) means that for every one - unit change in femur length (\(x\)), there is a corresponding change in expected height (\(y\)).

Answer:

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