# Section 2-6

# Point-Slope Form and Standard Form

POINT-SLOPE FORM

If you know the slope* m* of a line **and **the coordinates
(*x*_{1}, *y*_{1}) of one point on the line,
you can write the equation in point-slope form.

Example:

Find the equation of a line with slope **–**1/2 passing through the point (**–**3,
2).

Here, *m* = **–**1/2, *x*_{1} = **–**3, and *y*_{1} =
2, so the equation is:

or

STANDARD FORM

The standard form of a linear equation is

*A**x* + *By* = *C*.

The advantage of standard form is that it accomodates both horizontal lines (*A* = 0) and vertical lines (*B* = 0).

The disadvantage is that *A*, *B*, and *C* do not stand for anything obvious (like the slope or *y*-intercept). In fact, they are not unique: if we double them all, we get back the same line! You can check this with the following example.

*x* + 2*y* = 3

2*x* + 4*y* = 6

These two equations, both in standard form, represent the same line.