The most general form of a linear equation, in n-dimentional space, is y = sum(mixi) + c where the summation is over i = 1,2,3,...,n-1 The simpler (2-dimensional) version of the linear equation is y = mx + c where m is the slope and c is the y-intercept.
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y = mx + b
In general, a linear equation CANNOT be made to go through three points. That will only happen if the three points are collinear and in that case, the equation of the line will only require two points.
A linear equation has no higher powers than 1. This is linear.
To be a linear equation, the equation must be set equal to Y. Also, it can't have any square roots, or any variables on the bottom of a fraction. In general, the terms of a linear equation must be either first-degree polynomials with respect to the variables, constants, or products of the two. This disallows terms involving trigonometric, logarithmic, exponential, hyperbolic, and power expressions (except for the power of 1) and their inverses.
When it is a linear equation.