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Angle between two intersecting lines

The angle between two lines whose slopes are m1 and m2 is given by a formula such that tan q Description: 15549.png (where q is the angle between the lines)

Condition for two straight lines to be parallel

It can be visualized that two straight lines can be parallel only if they make an equal inclination with the X-axis. This will, in turn, ensure that their slopes are equal.

The lines y = m1x + c1 and y = m2x + c2 are parallel, if and only if m1 = m2.

Condition for two straight lines to be perpendicular

The General Equation of a line parallel to a given line ax + by + c = 0 will be ax + by + k = 0, where k is any constant which can be found by additional information given in the question.

The General Equation of a line perpendicular to a given line ax + by + c = 0 will be (bx - ay + k = 0) or (-bx + ay + k = 0), where k is any constant which can be found by additional information given in the question.
 
The lines y = m1x + c1 and y = m2x + c2 are perpendicular if and only if m1 m2 = -1.
 
Example
Which of the following cannot be the equation of the straight line parallel to the straight line 4x - 6y = 10?
  1. 2x - 3y = 8
  2. x - 1.5y = 2
  3. 8x + 12y = 12
  4. 2x - 3y = 4
Solution
Except option (c), all the other options can be written as 4x - 6y = K by multiplying the LHS by a suitable number. Hence, option (c) is the answer.
 





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