Noah has to read a book for a project. They have already read 105 pages, and they can read about 32 pages per day. Which of the following functions correctly relates the verbal information about the function to an algebraic equation?
y = 105x + 32
y = 32x
y = 32x − 105
y = 32x + 105
To find the correct function, let's break down the given information:
1. Noah has already read 105 pages.
2. Noah can read about 32 pages per day.
To relate this information to an algebraic equation, let's assign variables:
- Let y represent the total number of pages Noah has read (dependent variable).
- Let x represent the number of days that have passed (independent variable).
Since Noah has already read 105 pages, the initial value of y is 105. This eliminates the first and last options (y = 105x + 32 and y = 32x + 105) because they wrongly assume an initial value of 32 pages.
Next, we need to consider the rate at which Noah reads. Since Noah can read about 32 pages per day, the equation should include a term that represents this rate. This leaves us with the following equation:
y = 32x
Therefore, the correct function that relates the verbal information to an algebraic equation is y = 32x.