What is the standard form of linear equation in two variables?

Answer 1

The standard form of a linear equation in two variables, x and y, is

ax + by = k1 where a, b and k1 are constants.

This can be extended to three dimensions (x, y and z) simply:

ax + by + cz = k2 where a, b, c and k2 are constants.

Extension to 4 or more dimensions can be carried out in a similar way.

Apart from the fact that this form lends itself to simple extension to multi-dimensional space, the other main advantage is that the form is easy to represent in matrix form:

Thus AX = K where A is the matrix of coefficients, X the matrix of variables and k the matrix of constants. The tools of matrix algebra can then be used to work with these lines in hyperspace.

The standard form is sometimes confused with the slope-intercept form

y = ax + b.