Study Guide: Algebra Seminar
Session 7A: Different Forms of Linear Equations
Linear Equations
A linear equation is an equation for a straight line
These are all linear equations:
y = 2x+1
5x = 6+3y
y/2 = 3 - x
Let us look more closely at one example:
Example: y = 2x+1 is a linear equation:
The graph of y = 2x+1 is a straight line



When x increases, y increases twice as fast,
hence 2x (the 2 represents the slope of the line)
When x is 0, y is already 1. Hence +1 is also
needed (the 1 is the y-intercept of the line)
So: y = 2x + 1
Here are some example values:
x
y = 2x + 1
-1
y = 2 × (-1) + 1 = -1
0
y=2×0+1=1
1
y=2×1+1=3
2
y=2×2+1=5
Check for yourself that those points are part of the line above!
Finding Slope
From a Graph
Slope =
From 2 Points
Change in y (rise for + numbers, fall for –numbers)
Change in x (run forward for +numbers, back for –numbers)
Slope (m) =
Change in y yA-yB = 4-3 = 1
Change in x xA-xB 6-2 4
Different Forms
There are many ways of writing linear equations, but they usually have
constants (like "2" or "c") and must have simple variables (like "x" or "y").
Examples: These are linear equations:
y = 3x - 6
y - 2 = 3(x + 1)
y + 2x - 2 = 0
5x = 6
y/2 = 3
Slope-Intercept Form
The most common form is the slope-intercept equation of a straight line:
Example: y = 2x + 1
(Our example from the top, which is in Slope-Intercept form)
 Slope: m = 2
 Intercept: b = 1
Point-Slope Form
Another common one is the Point-Slope Form of the equation of a straight line:
y = y1 + m(x - x1)
Example: y =3 + ¼(x - 2)
 x1 = 2
 y1 = 3
m = ¼
(2,3) is a point on the line
¼ is the slope
General Form
And there is also the General Form of the equation of a straight line. This can be
found by manipulating (using balanced equations and your understanding of
number properties) an equation written in slope-intercept or point-slope form.
Ax + By = C
(A and B cannot both be 0)
Example: 3x + 2y=- 4
A = 3
From http://www.mathsisfun.com/algebra/linearB = 2
equations.html
 C = -4