SOLUTION: derive the condition for two lines with slope m1 and m2 to be parallel and perpendicular using the angel between two lines formula.

Question 1203322: derive the condition for two lines with slope m1 and m2 to be parallel and perpendicular using the angel between two lines formula.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

theta = = angle between two lines

One formula to use is

Parallel lines will have theta = 0.
This leads to tan(theta) = tan(0) = 0.
The right hand side is only zero when the numerator is zero.
which rearranges to
Therefore, parallel lines have equal slopes.
For example, the lines y = 3x+5 and y = 3x+7 are parallel. Each has slope of 3.

Perpendicular lines will involve theta = 90 degrees.
Use a unit circle to determine that tan(90) is undefined.
When it comes to "undefined", it means we have 0 in the denominator.
Division by zero is not allowed.
leads to which means we take the negative reciprocal of m1 to get m2, and vice versa.
An example pair of perpendicular slopes: and
Note that any pair of perpendicular slopes multiply to -1. Neither slope can be zero or undefined.

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