Question

winter jacket sales
the equation for the line of best fit is ( y = 3x + 75 ). according to the equation, which of these statements is true?
in a winter without any snow, the store would likely sell about 75 jackets.
the store sells about 75 jackets for each inch of snowfall.

Explanation:

Step1: Analyze the linear equation \(y = 3x+75\)

In the linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept), for the equation \(y = 3x + 75\), \(x\) represents the snowfall (in inches) and \(y\) represents the number of jackets sold.

Step2: Interpret the \(y\) - intercept

When \(x = 0\) (no snowfall, since \(x\) is snowfall in inches), we substitute \(x = 0\) into the equation \(y=3x + 75\). Then \(y=3\times0 + 75=75\).

Step3: Interpret the slope

The slope \(m = 3\). In the context of the problem, the slope means that for each additional inch of snowfall (\(x\) increases by 1), the number of jackets sold (\(y\)) increases by 3. The statement “The store sells about 75 jackets for each inch of snowfall” is incorrect because the slope \(m = 3\) (not 75).

Answer:

In a winter without any snow, the store would likely sell about 75 jackets.