How to detirmine if an equation is linear

Check that the y, or independent variable, is by itself on one side of the equation. If it is not, rearrange the equation so that it is. For example, given the equation 5y + 6x = 7, move the 6x term to the other side of the equation by subtracting it from both sides. This yields 5y = 7 - 6x. Then divide both side by 5 so you have y = 7/5 - (6/5) x.

Determine whether the equation is a polynomial or not. For an equation to be a polynomial, the power of the independent or "x" variable of each term must be a whole number. The terms can be made up of constants and variables. If the equation is not a polynomial, it is not a linear equation. In the example, y = 7/5 - (6/5) x has one "x" term and its power is 1. Because 1 is a whole number, y = 7/5 - (6/5) x is a polynomial

An equation is linear if the highest degree of x is 1.

For example y = 2x, y = 3x - 5 and y = 0.5x - 1 are all linear.

(y = x^2 - x is not linear because highest degree is 2)