Is 2x+7y=-12 linear or nonlinear

If you plot this on a graph it would be a linear equation ...

Answer: If you mean the mapping y (x) : = 3x+4, then y (x) is not linear, because it does not satisfy the two properties of linearity. Only equations of the form y (x) : = ax (for "a" being any real or complex number) are linear. Don't be confused with the plot of the graph of y (x) = 3x+4 being a line - this does not mean linear in the sense of the definition in Linear Algebra. Some authors define such function as "affine-linear".