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The (cartesian)
equation of a **straight line** is linear in the coordinates *x*
and *y*, that is, of the form
*ax*+*by*+*c*=0.

The **slope** of this line is -*a*/*b*, the **intersection with the
x-axis** (or

(In an **oblique coordinate
system** everything in the preceding paragraph remains true,
except for the value of the slope.)

When *a*+*b*=1 and *c*0 in the equation *ax*+*by*+*c*=0, the equation
is said to be in **normal form**. In this case *c* is the
**distance of the line to the origin**, and

= arcsin *a* = arccos *b*

is the angle that the perpendicular dropped to the line from the origin
makes with the positive *x*-axis (Figure 1).

**Figure 1:** The normal form of *L* is
*x* cos + *y* sin =*p*.

To reduce an arbitrary equation *ax*+*by*+*c*=0 to normal form, divide by
±, where the sign of the radical is chosen opposite
the sign of *c* when *c*0 and the same as the sign of *b* when
*c*=0.

Line of slope *m* intersecting the *x*-axis at *x*=*x*:

*y*=*m*(*x*-*x*)

Line of slope *m* intersecting the *y*-axis at *y*=*y*:

*y*=*mx*+*y*

Line intersecting the *x*-axis at *x*=*x* and the
*y*-axis at *y*=*y*:

*x*/*x*+*y*/*y*=1

(This formula remains true in **oblique coordinates**.)

Line of slope *m* going though (*x*,*y*):

*y*-*y*=*m*(*x*-*x*)

Line going through points (*x*,*y*) and (*x*,*y*):

(These formulas remain true in **oblique coordinates**.)

**Slope** of
line going through points (*x*,*y*) and (*x*,*y*):

(*y*-*y*)/(*x*-*x*)

Line going through points with **polar coordinates**
(*r*,) and (*r*,):

*r*(*r* sin(-)-*r* sin(-))=
*r**r* sin(-).

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.