For the function to be a linear, D. a = 20 because the rate of change is –3.
What is the Rate of Change of a Function?
The rate of change = change in y / change in x.
Therefore, for the function to be linear, the rate of change must be the same across the table of values.
Using, (4, 26) and (5, 23):
Rate of change = (26 - 23)/(4 - 5)
Rate of change = (3)/(1) = -3
Using (5, 23) and (6, a), we have:
(23 - a)/(5 - 6) = -3
(23 - a)/(-1) = -3
23 - a = (-3)(-1)
23 - a = 3
-a = 3 - 23
-a = -20
a = 20
Therefore, the answer is: D. a = 20 because the rate of change is –3.
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