Lines and Equations
Graphs of first degree equations in two variables will always be straight lines. There are many forms
of the equation for a straight line. You must be familiar with all of them but for the most part we will
use only the standard form, y-intercept form, and the STAT model form.
1. The equation of a straight line in standard form: Ax + By = C where A and B are not both 0 and
x and y are variables.
2. The equation can be solved for the y-intercept form: y = m x + b or
Given the slope m and a point P1(x1, y1) the point-slope form: is y = m (x − x1) + y1
3. The slope(m) can also be obtained if we are given two points on the line: P1 (x1, y1) and
P2 (x2, y2) using the formula or other methods:
Geometric interpretation of slope:
It is most important that everyone recognize the relation of the slope to the equation and to the
direction of the line. The slope represents the
RATE of the change of the vertical variable to the change of the horizontal variable.
You must be able to determine which are the vertical and horizontal variables and their amounts
and/or rates of change in applications.