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 2.402 in this context?

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

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

c the increase in a students femur length, in inches, for each increase of 23.34 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 equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(H = 2.402L+23.34\), \(H\) (height) is the dependent variable and \(L\) (femur length) is the independent variable.

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). In the context of \(H = 2.402L + 23.34\), \(m = 2.402=\frac{\Delta H}{\Delta L}\). This means that for a unit change in \(L\) (when \(\Delta L = 1\)), the change in \(H\) ( \(\Delta H\)) is \(2.402\).

Answer:

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