Question

the graph below shows a scatterplot and its line of best fit for data collected on the height and foot length of a sample of 10 male students.
height vs. foot length sample
the equation of the line of best fit is ( f = 1.5h - 4.3 ), where ( f ) is foot length in millimeters and ( h ) is height in centimeters.
explain the meaning of the slope in the context of the data
is the y - intercept reasonable for this context? explain.
use the model above to predict the height of a students with a foot measuring 245 millimeters

Explanation:

Step1: Substitute the value of \( F \) into the equation

We are given the equation \( F = 1.5h-4.3 \), and \( F = 245 \). Substitute \( F = 245 \) into the equation:
\( 245=1.5h - 4.3 \)

Step2: Solve for \( h \)

Add \( 4.3 \) to both sides of the equation:
\( 245 + 4.3=1.5h-4.3 + 4.3 \)
\( 249.3 = 1.5h \)
Then divide both sides by \( 1.5 \):
\( h=\frac{249.3}{1.5} \)
\( h = 166.2 \)

For the slope:
The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope. In the equation \( F = 1.5h-4.3 \), the slope \( m = 1.5 \). In the context of the data, for every 1 - centimeter increase in height (\( h \)), the foot length (\( F \)) increases by \( 1.5 \) millimeters.

For the \( y \) - intercept:
In the equation \( F = 1.5h-4.3 \), the \( y \) - intercept is \( - 4.3 \). A foot length of \( - 4.3 \) millimeters when height \( h = 0 \) is not reasonable in the context of measuring the height and foot length of students, because foot length cannot be negative.

Answer:

The height of the student is \( 166.2 \) cm. The slope of \( 1.5 \) means that for every 1 - centimeter increase in height, foot length increases by \( 1.5 \) mm. The \( y \) - intercept of \( - 4.3 \) is not reasonable as foot length cannot be negative.