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Definition: The linear function whose graph is this tangent plane, name L(x,y) = f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b) is called the linearization of f at (a,b) and the approximation f(x,y) ~= f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b) is called the linear approximation or tangent plane approximation of f at (a,b).
Source: Multivariable Calculus, 7th edition by James Stewart