Question

a group of biology students conducted an experiment to study the relationship between a persons femur length and the persons height. the given equation describes the relationship between the length ( l ), in inches, of a students femur and the students estimated height ( h ), in inches, for the students in the group. which of the following is the best interpretation of 2.411 in this context?

a the increase in a students estimated height, in inches, for each increase of 1 inch in the students femur length

b the increase in a students femur length, in inches, for each increase of 1 inch in the students estimated height

c the increase in a students femur length, in inches, for each increase of 23.07 inches in the students estimated height

d the estimated height, in inches, of a student whose femur has a length of ( l ) inches

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(H = 2.411L+23.07\), \(H\) (height) is the dependent variable (like \(y\)) and \(L\) (femur length) is the independent variable (like \(x\)).

Step2: Analyze the meaning of the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). In the context of \(H = 2.411L + 23.07\), the slope \(m = 2.411=\frac{\Delta H}{\Delta L}\).
When \(\Delta L = 1\) (an increase of 1 inch in femur length), \(\Delta H=2.411\times1\). This means that for each 1 - inch increase in femur length (\(L\)), the height (\(H\)) increases by \(2.411\) inches.

Answer:

A. The increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length