Math for Teachers
July 15, 2011
I. Forms of the equation of a line:
In all forms, x and y are variables and m stands for the slope.
UPPER AND LOWER CASES MATTER!
1. Slope-intercept form: y = mx + b
x and y are variables and m stands for the slope
b (LOWER CASE!!) stands for the y-intercept, where the graph of the line crosses the y-axis
This is both a working form and a final form, which means you can begin with this form and
leave your final answer in this form. This is the most common form for final answers.
2. Standard form: Ax + By = C or Ax + By + C = 0
x and y are variables and m stands for the slope
A, B and C are real numbers. In this class, A, B and C should be written as integers, with A
positive.
A
C
and the y-intercept by using b = .
B
B
This is a final form only. Do not begin with this form, but you can leave your answer in this
form.
The slope of this form can be found by using m = 
3. Point-slope form: y – y 1 = m( x – x 1 )
x and y are variables and m stands for the slope
(x 1 , y 1 ) is a point.
This is a working form only, which means you can begin with this form, but your final answer
should be either in slope-intercept or standard form.
II. Slope can be found by using the following formula:
Where (x 1 , y 1 ) is one point and (x 2 , y 2 ) is a different point:
m=
y 2  y1
x 2  x1
or m =
y1  y 2
x1  x2
III. Special equations:
1. A vertical line has an undefined slope, sometimes referred to as “no slope”. A vertical
line has an equation in the form of x = a, where a is the value of x or x 1 given in the problem.
2. A horizontal line has slope of zero or m = 0. A horizontal line has an equation in the form
of y = b, where b is the value of y or y 1 given in the problem.