Question

The table below shows the number of jumping jacks completed after a given period of time in minutes.

Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200


Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50

Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50

What is the slope of the line that connects the 3rd and 4th point?
50

What is the slope of the line that connects the 1st and the 4th point?
50

Is the common difference (aka slope aka rate of change) constant?
Yes

Why is it or is it not constant?
It is constant because it is a linear function.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The common difference, which is also the slope or rate of change, is constant because the table represents a linear function. In a linear function, the change in the dependent variable (in this case, the number of jumping jacks) is consistent for each unit increase in the independent variable (in this case, the time in minutes). Therefore, the common difference remains constant at 50.