Parallel lines:
 Two lines are parallel if and only if they have the same slope. They never intersect.
 If m_{1} is the slope of one line and m_{2} is the slope of another line then m_{1} = m_{2}
Perpendicular lines:
 Two lines are perpendicular if and only if the product of their slopes is  1, or if one is vertical and the other horizontal.
 They meet at a point to form right angles.
 They have negative reciprocal slopes.
The Product of the perpendicular lines slopes are equal to 1
i.e., m_{1} and m_{2} are slopes of two perpendicular lines and their product m_{1}m_{2} = 1
i.e., m_{1} = 1/(m_{2})
Parallel lines  Perpendicular lines 
y = 2x + 5 y = 2x  5 y = 2x + 7 y = 2x + 115  y = 4x + 11 y = 1/4x  2 
These lines are all parallel. They all have the same slope m = 2.  These lines are perpendicular.
Their slopes (m) are negative reciprocals.

Examples:
 Find the equation of the line passing through (5,4) and parallel to 3x  y  15 = 0.
solution:
Any line parallel to 3x  y  15 = 0 takes the form of 3x  y + k = 0.
Note:
For any equation of two parallel lines differ in constant terms, x and y coefficients being same.
If 3x  y + k = 0 passing through (5,4), we have
3.5  4 + k = 0
15  4 + k = 0
11 + k = 0
Therefore, k = 11
The required equation is 3x  y  11 = 0.
 Find the equation of a line perpendicular to 3x  4y + 1 = 0 and passing through (2,4).
Solution:
Given that,
3x  4y + 1 = 0, Slope of this equation is m_{1} = (xcoefficient / ycoefficient).
= 3/4
= 4/4
Let the slope of the line perpendicular to 3x  4y + 1 = 0 be m_{2}
We know that product perpendicular lines slopes are equal to 1
i.e., m_{1}m_{2} = 1
We know m_{1} = 3/4
(3/4)m_{2} = 1
m_{2} = 4/3
The slope of line required is 4/3 and a point on the line is (2,4).
By the point slope form of a line we have,
(y  y_{1}) = m (x  x_{1})
y  4 = 4/3(x  2)
3y  12 = 4x + 8
4x + 3y  20 = 0
This is the required line.
Note:
The equation of x axis or horizontal line is y = 0. The slope is 0.
The equation of y axis or vertical line is x = 0. The slope is not defined.
Directions: Answer the following questions. Also write at least 10 examples of your own.
