# Angle between two intersecting lines

The angle between two lines whose slopes are m

_{1}and*m*_{2}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*= m

_{1}

*x*+

*c*

_{1}and

*y*=

*m*

_{2}

*x*+

*c*

_{2}are parallel, if and only if

*m*

_{1}=

*m*

_{2}.

# Condition for two straight lines to be perpendicular

The

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*=*m*_{1}*x*+*c*_{1}and*y*=*m*_{2}*x*+*c*_{2}are perpendicular if and only if*m*_{1}*m*_{2}= -1.Example

Which of the following cannot be the equation of the straight line parallel to the straight line 4

*x*- 6*y*= 10?- 2x - 3y = 8
- x - 1.5y = 2
- 8x + 12
*y*= 12 - 2
*x*- 3*y*= 4

Solution

Except option (c), all the other options can be written as 4

*x*- 6*y*=*K*by multiplying the LHS by a suitable number. Hence, option (c) is the answer.