# 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(x_{1}, y_{1}) the point-slope form: is y = m (x − x_{1}) + y_{1}
3. The slope(m) can also be obtained if we are given two points on the line: P_{1} (x_{1}, y_{1}) and
P_{2} (x_{2}, y_{2}) 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. |