Question

Which of these is an example of a linear equation?

`6x+9y=5`
`x^2-y^3=1`

Answer 1

Linear equation: `6x+9y=5`

Non-linear equation: `x^2-y^3=1`

Explanation:

A linear equation is one where the only degree of any variable in the equation is 1 (no squares, cubes, square roots, etc.). A graph of any such equation will have no "curvature" to it at all. One variable is expressible as a sum of multiples of the other variables (plus a possible constant), resulting in a flat line/plane (hence "linear").

A sample graph of the linear equation `6x+9y=5`:

graph{6x+9y=5 [-10, 10, -5, 5]}

A non-linear equation is any equation that has at least one variable with an exponent other than 1 in it. A graph of any non-linear equation will have curvature (i.e. it will not be straight everywhere).

A sample graph of the non-linear equation `x^2-y^3=1`:

graph{x^2-y^3=1 [-10, 10, -5, 5]}