Comparing Averages: Slope Between Two Points

[alliereid]

Homework Statement

What can you conclude about average slope between two points and the slopes of the individual line segments on which the points lie?

Homework Equations

The Attempt at a Solution

I thought that the average slope slope numerical answer is in between the slopes of the two points but the question is worth two marks so there must be another fact to it.

 

[dontdisturbmycircles]

I think that what they are trying to get at is this:

Given any curve between two points, how does the average value of the slope compare to the slope that would be found by drawing a straight line between the points.

Hint: If it is known that bob runs 5km north in one hour, with no knowledge about his speed or direction at any time within that hour, can we still conclude something about his average velocity?

 

[Blueshift5]

I would suggest that the average slope between two points is a representation of the overall trend or direction of change between those two points. It takes into account the slopes of the individual line segments, but also considers the distance and direction between the points. Therefore, while the average slope may fall between the slopes of the individual line segments, it is not necessarily a direct average of those slopes. Additionally, the average slope may provide a more accurate picture of the overall change between the two points, rather than just focusing on the individual line segments. It is important to consider both the average slope and the individual slopes in order to fully understand the data and make informed conclusions.