The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods.

Answer 1

In the context of the data collected by Nicholas, the slope and y-intercept can be interpreted as follows:

1. Slope (-63): The slope of -63 indicates that for each additional day (x), the number of canned goods (y) collected decreases by 63. This negative value suggests that as time progresses, the total number of canned goods is declining. This could imply that cans are being used up or taken away at a rate of 63 cans per day.

2. Y-Intercept (825): The y-intercept, which is 825, represents the initial amount of canned goods collected when x (the number of days) is 0. In other words, at the start (day 0), Nicholas had 825 canned goods available.

Putting it all together: At the beginning of the observation period, Nicholas started with 825 canned goods. However, over time, at a rate of 63 cans per day, the number of available canned goods decreases. This reflects a situation where canned goods are being used or depleted consistently over the course of the days measured.