Question

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 rates 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.

Answer 1

Answer: a. The rate of change in this situation represents the average number of pages read per minute. From the table, it can be seen that the rate of change is constant, as the ratio of the change in y (pages) to the change in x (minutes) is always the same.

For example, when x increases from 0 to 5, y increases from 0 to 25, so the rate of change is 25/5 = 5 pages per minute.

b. To represent the total number of pages as it relates to the number of minutes read, a linear equation can be used. The slope of the line represents the rate of change, and the y-intercept represents the number of pages read when x is equal to 0 (minutes).

Using the rate of change from the above example (5 pages per minute), the equation can be written as y = 5x + 0, where x represents the number of minutes and y represents the total number of pages read.

Explanation: