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Linear graphs make straight lines. Non-linear graphs make thins like parabolas, hyperbolas, and ellipses
The word linear means in a straight line. If the graph is a line, it is linear. Also, linear equations are of the first order; they contain a variable but not a square (or higher power) of a variable. If the equation contains x2 it is not linear.
Linear describes a relationship that exhibits a straight line when plotted on a graph, for example. Non liner is any thing other than a straight line.
A linear relation is a straight line. A non-linear relation is not - it mayor may not be be a curve.
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.