What is the standard form equation?

Linear it is Ax + By = C

This can be algebraically rearranged to :-

By = -Ax + C

or

y = (-A/B)x + C/B

or

Ax + By + C = 0

Other conic forms are

Parabola Ax^2 + Bx + C = 0

Circle Ax^2 + By^2 + 2Ax + 2By + C = 0

Ellipse

x^2 /a^2 + y^2/b^2 = 1