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?
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?
What is the slope of the line that connects the 3rd and 4th point?
What is the slope of the line that connects the 1st and the 4th point?
Is the common difference (aka slope aka rate of change) constant?
Why is it or is it not constant?
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The common difference is 50.
The slope of the line connecting the first two points is (100-50)/(2-1) = 50/1 = 50.
The slope of the line connecting the third and fourth points is (200-150)/(4-3) = 50/1 = 50.
The slope of the line connecting the first and fourth points is (200-50)/(4-1) = 150/3 = 50.
Yes, the common difference (slope) is constant.
The common difference is constant because each additional minute corresponds to an additional 50 jumping jacks. Therefore, for every additional minute, the number of jumping jacks increases by 50, resulting in a constant rate of change/slope.