Question

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.

Answer 1

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.