Question

1. the graph shows the linear relationship between number of bagels a bagel shop has remaining, and the number of customers served so far that day. find the rate of change of bagels remaining with respect to the number of customers served.

Explanation:

Step1: Identify two points on the line

Let's take the points \((10,200)\) and \((30,100)\) from the graph.

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 10,y_1=200,x_2 = 30,y_2 = 100\) into the formula:
\(m=\frac{100 - 200}{30 - 10}\)
\(m=\frac{-100}{20}\)
\(m=- 5\)

Answer:

The rate of change is \(-5\) (which means for each additional customer served, the number of bagels remaining decreases by \(5\)).