Question

winter storms
the equation for the line of best fit is $y = \frac{2}{3}x + \frac{1}{3}$. according to the equation, which of these statements is true?
the shoveling time increases by about 3 hours for every 2 inches of snowfall.
the shoveling time increases by about 2 hours for every 3 inches of snowfall.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=\frac{2}{3}x+\frac{1}{3}\), \(m = \frac{2}{3}\).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(y\) represents shoveling time (in hours) and \(x\) represents snowfall (in inches). So, \(m=\frac{2}{3}=\frac{\text{Change in }y}{\text{Change in }x}\), which means for a change in \(x\) (snowfall) of \(3\) inches, the change in \(y\) (shoveling time) is \(2\) hours.

Answer:

The shoveling time increases by about 2 hours for every 3 inches of snowfall.