Question

the scatter plot and line of best fit below show the length of 7 peoples femur (the long leg bone in the thigh) and their height in centimeters. what does the slope of the line represent? answer the expected femur length when the height is 1 centimeter. the change in expected height for every one additional centimeter of femur length. the change in expected femur length for every one additional centimeter of height. the expected height when the femur has a length of 1 centimeter.

Explanation:

Step1: Recall the concept of slope in a linear relationship

In a linear equation \(y = mx + b\) (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 the scatter - plot, the y - axis represents height (dependent variable) and the x - axis represents femur length (independent variable).

Step2: Interpret the slope

The slope formula \(\text{slope}=\frac{\text{Change in }y}{\text{Change in }x}\). Here, \(y\) is height and \(x\) is femur length. So, the slope represents \(\frac{\text{Change in height}}{\text{Change in femur length}}\), which means the change in expected height for every one additional centimeter of femur length.

Answer:

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