Question

Monique is reading a book. The table shows how the number of pages remaining in the book is changing over time.

Time (hours) Number of Pages Remaining
0 360
1 320
2 280
3 240
4 200
Which equation describes the relationship between t, the time in hours, and N, the number of pages remaining in the book?

A. N = -40t - 360
B. N = -40t + 360
C. N = 40t + 360
D. N = 40t - 360

Answer 1

To find the equation that describes the relationship between \( t \) (time in hours) and \( N \) (number of pages remaining), we first notice how the number of pages changes with time.

From the table:
- At \( t = 0 \), \( N = 360 \)
- At \( t = 1 \), \( N = 320 \)
- At \( t = 2 \), \( N = 280 \)
- At \( t = 3 \), \( N = 240 \)
- At \( t = 4 \), \( N = 200 \)

We can see that as \( t \) increases by 1 hour, \( N \) decreases by 40 pages. This indicates a linear relationship where the first change in \( N \) (i.e., the slope) is \( -40 \).

Let's identify the general equation of a line in slope-intercept form:
\[
N = mt + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.

From the data:
- The slope \( m = -40 \)
- The y-intercept \( b \) is the initial value when \( t = 0 \), which is \( N = 360 \).

Thus, the equation becomes:
\[
N = -40t + 360
\]

So, the correct choice is:
**B. \( N = -40t + 360 \)**.