Chapter 4, Problem 12STP

To determine

To explain:The identification of two lines as parallel or perpendicular lines.

Answer to Problem 12STP

The parallel or perpendicular relation between the lines can be established with the help of calculating the slopes.

Explanation of Solution

The lines in the Cartesian co-ordinates may have some relation with each other. The lines may be parallel or perpendicular. This can be identified by plotting the graph on the Cartesian plane. But plotting the graph to find the parallel or perpendicular relation is not the always handy option. The relation between the lines can just be identified with the help of calculating the slopes of the given lines.

Condition for parallel lines: The two lines are said to be parallel if the slopes of these two lines is equal.

  $m_1=m_2$

Condition for perpendicular lines: The lines become perpendicular when the slopes are connected with the following relation.

  $m_1{m}_2=-1$

Therefore, the lines can be identified as parallel or perpendicular by calculating the slopes of the lines and then checking for the conditions of parallel lines and the perpendicular lines.