Section 2-6
Point-Slope Form and Standard Form
POINT-SLOPE FORM
If you know the slope m of a line and the coordinates
(x1, y1) 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, x1 = –3, and y1 =
2, so the equation is:
or
STANDARD FORM
The standard form of a linear equation is
Ax + 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 + 2y = 3
2x + 4y = 6
These two equations, both in standard form, represent the same line.
