To check: The lines are parallel at given slopes and .
The lines are parallel if .
The slope is the measure of the angle of a line from the horizontal. Since parallel lines must have the same angle, then parallel lines have same slope and the lines that have the same slope are parallel that is,
Thus, the slope of parallel lines are equal that is .
To check: Whether the lines are perpendicular at given slopes and .
The lines are perpendicular if
Perpendicular lines having negative slope, because it will have to be a decreasing line, So the perpendicular lines have slopes which have opposite signs that means perpendicular slopes is that their values are reciprocal.
Thus, The slope of perpendicular line is the negative reciprocal of the slope of the original line that is .
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