Question

birthday party
the equation for the line of best fit is $y = -\frac{3}{5}x + 49$. according to the equation, which of these statements is true?
the number of juice boxes is decreasing by about 3 boxes every 5 minutes.
the number of juice boxes is decreasing by about 5 boxes every 3 minutes.

Explanation:

Step1: Analyze the slope of the linear equation

The equation of the line is \(y =-\frac{3}{5}x + 49\). In the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept), the slope \(m =-\frac{3}{5}\). The slope represents the rate of change of \(y\) (number of juice boxes) with respect to \(x\) (time in minutes).

Step2: Interpret the slope

The slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(m =-\frac{3}{5}\), which means that for every increase of \(\Delta x = 5\) units in \(x\) (time), \(\Delta y=- 3\) units (the number of juice boxes). So, the number of juice boxes is decreasing by 3 boxes every 5 minutes.

Answer:

The number of juice boxes is decreasing by about 3 boxes every 5 minutes.