Question

endurance tamika wants to improve her running endurance and thus tries to run for longer periods of time each day. the distance she runs, given the day, is provided in the table.

day	1	2	3	4	5	6	7
distance	2	2.25	2.75	3.5	4	4.5	5

a. determine linearity.
select choice
select choice
linear
nonlinear

Explanation:

Step1: Calculate first - differences

For day 1 to day 2: $2.25 - 2=0.25$; for day 2 to day 3: $2.75 - 2.25 = 0.5$; for day 3 to day 4: $3.5 - 2.75=0.75$; for day 4 to day 5: $4 - 3.5 = 0.5$; for day 5 to day 6: $4.5 - 4=0.5$; for day 6 to day 7: $5 - 4.5 = 0.5$.

Step2: Check for constant first - differences

The first - differences are not constant ($0.25,0.5,0.75,0.5,0.5,0.5$). In a linear relationship, the first - differences between consecutive $y$ - values (distance in this case) for equally - spaced $x$ - values (days) should be constant.

Answer:

nonlinear