Linear and quadratic equations are the types of equations most commonly encountered in high school algebra and in real life applications. They are different from each other in a number of key ways.
Linear equations are in the form y = mx + b, whereas quadratic equations have a variable that is squared, so they are in the form y = ax^2 + bx + c.
The graph of a linear equation on an x-y coordinate plane is a straight line. A quadratic equation results in a graph shaped like a parabola.
A common task with linear equations is finding the line's slope, which is equal to m in the equation y = mx + b. A quadratic equation's slope is always changing because the parabola is curved.
Solving linear equations only requires simple algebra of adding, subtracting, multiplying, and dividing. Quadratic equations are solved by more complicated processes of factoring, finding square roots, or using the quadratic formula.
When given a y value, a linear equation will result in only one solution for an x value. A quadratic equation can have two solutions for x when given a y value.