The common difference is 50.
The slope of the line connecting the first two points (1, 50) and (2, 100) would be (100-50)/(2-1) = 50.
The slope of the line connecting the third and fourth point (3, 150) and (4, 200) would also be 50.
The slope of the line connecting the first and fourth point (1, 50) and (4, 200) would be (200-50)/(4-1) = 50.
The common difference (slope) is constant, because the increase in the number of jumping jacks (x-value) results in a consistent increase in the number of repetitions (y-value). Each time the x-value increases by 1, the y-value increases by 50, resulting in a constant rate of change/slope.
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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