Question

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?
150

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

Explanation:

The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.

The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.

The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.

The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.