Jackie wants to justify that f (x) = 2x - 6 is a linear function. If she evaluated F (x) for consecutive integer values, write a statement to justify her claim of f (x) = 2x - 6 as a linear function.

Jackie wants to justify that f (x) = 2x - 6 is a linear function.

Lets assume some values for x and find out f (x)

We make a table with x values 1, 2, 3, 4 and find f (x)

To find f (x) we plug in x value in the given equation

x f (x)

1 2 (1) - 6 = - 4

2 2 (2) - 6 = - 2

3 2 (3) - 6 = 0

14 2 (4) - 6 = 2

for f (x) we got - 4, - 2, 0, 2

The value of f (x) is increasing by 2. There is a constant increase in f (x)

When there is a constant rate of increase then it is a linear function

constant rate of increase that is slope = 2. Hence f (x) = 2x - 6 is a linear function.