SOLUTION: Find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. Use y for the dependent variable and all

Algebra ->  Linear-equations -> SOLUTION: Find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. Use y for the dependent variable and all       Log On


   

Question 896090: Find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. Use y for the dependent variable and all letters in lower case.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Keeping the slope of the given line as m, let M=-%281%2Fm%29, and M is the slope for any line perpendicular to y=mx+b.

Also notice b=y-mx.

The wanted line parallel:
highlight%28y=mx%2B%28c-m%2Aa%29%29.

The wanted line perpendicular:
highlight_green%28y=Mx%2B%28c-Ma%29%29
but in case you want this in terms of m of the given equation,
y=-%281%2Fm%29x%2B%28c-%28-%281%2Fm%29%29a%29
highlight%28y=-x%2Fm%2B%28c%2Ba%2Fm%29%29