Question

caleb is hosting an outdoor birthday party, and he wants to make sure he has enough juice boxes to last the entire party. he keeps track of the number of juice boxes remaining throughout the party. this scatter plot shows the data he collected and the line of best fit. 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 5 boxes every 3 minutes. the number of juice boxes is decreasing by about 3 boxes every 5 minutes.

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, the equation of the line of best fit is $y=-\frac{3}{5}x + 49$. The slope $m =-\frac{3}{5}$.

Step2: Interpret the slope

The slope represents the rate of change. In the context of the problem, $x$ is time in minutes and $y$ is the number of juice boxes. A slope of $-\frac{3}{5}$ means that for every increase of 5 units in $x$ (5 minutes), $y$ (the number of juice boxes) decreases by 3 units.

Answer:

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