Question

1. michelle reads a book for the school read - a - thon. the table shows the proportional relationship between x, the number of minutes and y, the total number of pages read.

a. determine the rate of change and explain its meaning in the context of this situation.
b. write an equation to represent the total number of pages as it relates to the number of minutes read.

Explanation:

Step1: Calculate the rate of change

The rate of change (slope) \(m\) for a proportional relationship \(y = mx\) is given by \(m=\frac{y}{x}\). Using the first pair \((x = 30,y = 15)\), \(m=\frac{15}{30}=\frac{1}{2}\).

Step2: Explain the rate of change

The rate of change \(\frac{1}{2}\) means that Michelle reads \(\frac{1}{2}\) of a page per minute.

Step3: Write the equation

Since \(y = mx\) and \(m=\frac{1}{2}\), the equation is \(y=\frac{1}{2}x\).

Answer:

a. The rate of change is \(\frac{1}{2}\). It means Michelle reads \(\frac{1}{2}\) page per minute.
b. \(y=\frac{1}{2}x\)