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?
Skip to navigation
Auto saved at: 13:32:31
English
The common difference between the number of jumping jacks completed is 50.
For the first two points (1, 50) and (2, 100), the slope of the line connecting them is (100-50)/(2-1) = 50.
For the 3rd and 4th point, (3, 150) and (4, 200), the slope of the line connecting them is (200-150)/(4-3) = 50.
For the 1st and 4th point, (1, 50) and (4, 200), the slope of the line connecting them is (200-50)/(4-1) = 50.
The common difference, or slope, is constant at 50. This is because in each case, we are adding 50 jumping jacks per minute, which results in a consistent rate of change throughout the table.