The table represents a linear function because there is a pattern for the x-coordinates and y-coordinates.

The table represents a linear function because the ratio of the change in the y value and the change in the x value is constant.

The table represents a nonlinear function because the ratio of the change in the y value and the change in the x value is not constant.

The table does not represent a function because there is more than one output for at least one input.

Equations 1 and 2, only

Equations 1 and 4, only

Equations 2 and 3, only

Equations 1, 3, and 4, only

x - 3y=12

y=x³

3y=x

y=5x²+6x

4x+3y²=24

y = 2x³ - x² + 5

y = 5x - 19

14x - 8 = 2y

3y = 6x + 15

y= 3x-4

y=9x²+7x

y=x

y=2x³

2x²=y+4

Linear function

Nonlinear function

Function I, only

Function II, only

Function I and Function II, only

Function I, Function II, and Function III

Graph I, only

Graph II, only

Graph I and Graph II, only.

Graph I, Graph II, and Graph III

Both Graphs have multiple y intercepts

Both graphs are not functions

The first graph is linear because it has a constant rate of change.

The second graph is nonlinear but has a constant rate of change.