Equation of Straight Line in Plane/General Equation/Also presented as

General Equation of Straight Line in Plane: Also presented as

Some sources give the general equation of the straight line in the plane as:

$a x + b y + c = 0$

where $a, b, c \in \R$ are given, and not both $a, b$ are zero.

Its equivalence to the given form can be seen by equating $a = \alpha_1, b = \alpha_2, c = -\beta$.

Similarly equivalent forms include:

$a x = b y + c$

and so on.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $3$.
• 1958: P.J. Hilton: Differential Calculus ... (previous) ... (next): Chapter $1$: Introduction to Coordinate Geometry: $(1.2)$
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 10$: Formulas from Plane Analytic Geometry: General Equation of Line: $10.7$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): line: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): line: 2.
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Cartesian coordinates
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 8$: Formulas from Plane Analytic Geometry: General Equation of Line: $8.7.$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): straight line (in the plane)