Question

the scatter plot shows the heights and shoe sizes of some students. heights and shoe sizes the equation for the line of best fit is $y = \frac{1}{3}x - 13$. which statement best interprets the slope of the line of best fit? for every 3 - inch increase in height, shoe size decreases by 1 size. for every 3 - inch increase in height, shoe size increases by 1 size. for every 1 - inch increase in height, shoe size increases by 3 sizes. for every 1 - inch increase in height, shoe size decreases by 3 sizes.

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(y=\frac{1}{3}x - 13\), the slope \(m=\frac{1}{3}\).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(y\) represents shoe size and \(x\) represents height. If \(\Delta x = 3\) (a 3 - inch increase in height), then \(\Delta y=\frac{1}{3}\times3 = 1\) (a 1 - size increase in shoe size).

Answer:

For every 3 - inch increase in height, shoe size increases by 1 size.