Three special types of lines
1. Horizontal lines, m = 0 
2. Vertical lines, mundefined 
3. Lines through the origin, b = 0 
1. Horizontal lines, m=0
Horizontal (y = b)
(For every xvalue) 
m = 0 (Zero) 

Every point on a horizontal line has the same second number, for all xvalues.
Example 1: Find the equation of the line
if m = 0 and b =  3.
Equation: y =  3

Example 2:
Given two points with the same
second number: (2, 5), ( 7, 5)
Equation: y = 5 


2. Vertical lines, mundefined
2. Vertical (x = a)
(For every yvalue) 
m = (Not Defined) 

Every point on a vertical line has the same first number, for all yvalues.
Example 1:
Find the equation of the line
if a = 4. m is undefined
Equation: x = 4

Example 2:
Given two points with the same
first number: ( 7, 5), ( 7,  3)
Equation: x =  7 


3. Lines through the origin: y = m x → [ b = 0 ]
If a line goes through the origin the yintercept is (0, 0), and b = 0
y = m x
The Line is: 
The Slope is: 
Example 
Rising as x moves from left to right 
m > 0, (Positive)


Falling as x moves from left to right 
m < 0, (Negative) 

Note1: Since one point is the origin (0, 0), the slope to the other point (x_{1} , y_{1}) is the ratio m = y_{1} / x_{1}
Note2: Since one point is the origin (0, 0), if the slope is the ratio
m = y_{1} / x_{1} then another point is (x_{1} , y_{1}).
Example 1:
Equation: y = 5/2 x, m > 0

Example 2:
Equation: y =  2/3 x, m < 0

From (0, 0)
the second number is: (2, 5) or ( 2,  5)

From (0, 0)
the second number is: (3,  2) or ( 3, 2) 


