Question

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

Explanation:

Step1: Analyze the slope and y-intercept

The equation of the line of best fit is \( y = 3x + 75 \). In the slope - intercept form \( y=mx + b \), \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value when \( x = 0 \)).
Here, the slope \( m = 3 \), which means for each increase of 1 in \( x \) (each inch of snowfall), \( y \) (number of jackets sold) increases by 3. The y - intercept \( b=75 \), which is the value of \( y \) when \( x = 0 \) (when snowfall \( x = 0 \) inches).

Step2: Evaluate the first statement

The first statement says "The store sells about 75 jackets for each inch of snowfall". But the slope \( m = 3 \), so the rate of change of jackets sold per inch of snowfall is 3, not 75. So this statement is false.

Step3: Evaluate the second statement

The second statement says "In a winter without any snow, the store would likely sell about 75 jackets". When there is no snow, \( x = 0 \) (since \( x \) represents snowfall in inches). Substitute \( x = 0 \) into the equation \( y=3x + 75 \). We get \( y=3(0)+75=75 \). So when \( x = 0 \) (no snowfall), the number of jackets sold \( y = 75 \). This statement is true.

Answer:

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