Question

Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B?

Answer 1

Answer: The initial values of the two functions are different but the rate of change is same.

Step-by-step explanation:

For function  A ,  

When x=1, the initial value of function A=3

The rate of change of function A =$\frac{y_2-y_1}{x_2-x_1}=\frac{7-3}{3-1}=\frac{4}{2}=2$

For function B,  

When x=1, the initial value of function B= 4

The rate of change of function A =$\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{3-1}=\frac{4}{2}=2$

Since, 3≠4, thus, the initial values of two function is different.

But the rate of change is same.

Thus, Function A has odd output values, because it has an odd number as initial value and 2 as constant rate of change.

Function B has even output values, because it has an even number as initial value and 2 as constant rate of change.

Answer 2

I would say:
The initial values of the two functions are different, and the rates of change of the two functions are the same.

(AKA B)