Question 1203322
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theta = {{{theta}}} = angle between two lines


One formula to use is
{{{tan(theta) = abs((m[1]-m[2])/(1 + m[1]m[2]))}}}


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. 
{{{m[1]-m[2] = 0}}} which rearranges to {{{m[1] = m[2]}}}
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.
{{{1 + m[1]m[2] = 0}}} leads to {{{m[2] = -1/(m[1])}}} which means we take the negative reciprocal of m1 to get m2, and vice versa.
An example pair of perpendicular slopes: {{{m[1] = 5/7}}} and {{{m[2] = -7/5}}}
Note that any pair of perpendicular slopes multiply to -1. Neither slope can be zero or undefined.
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