Question

a restaurant owner sets a jar of peppermints at the front of his store each day. he made a scatter plot that shows the number of peppermints left in the jar compared to the number of hours the restaurant had been opened that day. which is the best interpretation of the slope of the trend line shown? a. there are about 50 less peppermints every 2 additional hours the store is open. b. there are about 25 less peppermints every additional hour the store is open. c. there are about 25 less peppermints every 2 additional hours the store is open. d. there are about 50 less peppermints every additional hour the store is open.

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the trend - line. For example, when \(x_1 = 0,y_1=175\) and when \(x_2 = 2,y_2 = 150\). Then \(m=\frac{150 - 175}{2-0}=\frac{- 25}{2}=-12.5\). In terms of interpretation, for a change in \(x\) (hours) of \(2\), the change in \(y\) (number of peppermints) is \(-25\).

Step2: Interpret the slope

The slope \(m = - 12.5\) means that for every \(2\) additional hours (\(\Delta x=2\)), the number of peppermints (\(\Delta y\)) decreases by \(25\).

Answer:

C. There are about 25 less peppermints every 2 additional hours the store is open.