# 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  (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.