Question

For each function, state whether it is linear.

Function 1
{(4,0), (6, 4), (8, 8), (10, 12)}
A Linear
B Not linear

Answer 1

The function given by the set {(4,0), (6, 4), (8, 8), (10, 12)} is linear because the change in y-values is consistent as the x-values increase by the same amount.

Step-by-step explanation:

The question asks whether the given function is linear. A linear function has a constant rate of change, which means the difference between the y-values should be consistent when the x-values change by a consistent amount. To determine if the function is linear, we can look at the differences between successive y-values and see if they are constant as the x-values increase by a consistent amount.In the set {(4,0), (6, 4), (8, 8), (10, 12)}, the x-values increase by 2 each time. Let's look at the rates of change between each pair of points:

Between (4,0) and (6,4), the change in y is 4 - 0 = 4.

Between (6,4) and (8,8), the change in y is 8 - 4 = 4.

Between (8,8) and (10,12), the change in y is 12 - 8 = 4.

The change in y is consistent (4 each time) while x increases by the same amount (2 each time). This indicates that the function has a constant rate of change, and therefore, it is linear.