For this case we observe that the first table has a constant rate of change.
In linear functions, the rate of change is constant.
To prove it, we will find the rate of change for two different intervals.
Interval 1:
[tex] m = \frac{1-\frac{1}{2}}{2-1} [/tex]
[tex] m = \frac{\frac{1}{2}}{1} [/tex]
[tex] m = \frac{1}{2} [/tex]
Interval 2:
[tex] m = \frac{2-\frac{1}{2}}{4-1} [/tex]
[tex] m = \frac{\frac{3}{2}}{3} [/tex]
[tex] m = \frac{3}{6} [/tex]
[tex] m = \frac{1}{2} [/tex]
Since the rate of change is constant, then the function is linear.
Answer:
The first table is a linear function.
