What graph's equation is a line?

Answer 1

A linear equation.

In n-dimensional space, it is of the form

A(0) + A(1)X(1) + ... + A(n-1)X(n-1) + A(n)X(n) = 0

where A(0), A(1), ... A(n) are coefficients and X(1), ... X(n) are the variables.

Normally the 0, 1, ... n would be written as suffices but this browser does not support such mathematically essential features!

In 2-dimensional space, the equation becomes

A(0) + A(1)X(1) + A(2)X(2) = 0

If you rewrite X(1) = X and X(2) = Y,

you get A(0) + A(1)X + A(2)Y = 0

which can be rearranged to A(2)Y = -A(1)X + A(0)

Then, dividing through by A(2) and writing m = -A(1)/A(2) and c = A(0)/A(2) gives

Y = mX + c - the slope-intercept form of the equation of a straight line in 2 dimensions.