Hi Nick,

A linear equation with one variable $x$ is an equation of the form $y = a x + b$ where $a$ and $b$ are constants. If you fix $a$ and $b$ the graph of this equation is a straight line. Hence a linear equation.

The equation $y = 2 x^2 - 3x + 7$ is not a linear equation since it has an $x^2$ term and cant be written as $y = a x + b.$

I hope this helps,
Penny