How do you determine if a relation or equation is linear?

Question

How do you know when a relation or equation is linear?

Examples if needed:

relation: [(-1,-2),(0,0),(1,2),(2,4)]

[(-1,-1),(0,-1),(1,-1),(2,-1)]

equation: 3x + y = 20

y = x * x (y = x(to the 2nd power))

Answer 1

A relationship is linear if, for a constant change in one variable there is a corresponding constant change in all other variables.  An equation is linear iff all the variables are to the 1st power.

Both your example relationships are linear:

For the 1st, for each +1 change in the "x" value, there is a corresponding +2 change in the "y" variable.

For the 2nd relationship, for each +1 change in the "x" value, there is 0 change in the "y" variable.

The 1st equation is linear because x and y are both to the 1st power.

The 2nd equation is non-linear because x has an exponent other than 1.