SOLUTION: Perpendicular to y=-2x-4 and passes through (1,0). Plz give me formula and work... I'm using this as a guide for my homework.

Algebra ->  Linear-equations -> SOLUTION: Perpendicular to y=-2x-4 and passes through (1,0). Plz give me formula and work... I'm using this as a guide for my homework.      Log On


   

Question 893571: Perpendicular to y=-2x-4 and passes through (1,0).
Plz give me formula and work... I'm using this as a guide for my homework.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=mx%2Bb ------ slope is m, and y intercept is (0,b).
You can solve the form for b to have:
b=y-mx

You are asking specifically for a FORMULA to use for finding the line perpendicular to some
line y=mx+b and containing a specific point.

A line highlight_green%28y=mx%2Bb%29 will be perpendicular to another line highlight_green%28y=Mx%2Bk%29 if m%2AM=-1.
This means that the line perpendicular to y=mx%2Bb will be highlight_green%28y=-%281%2Fm%29x%2Bk%29.

If now given that this line y=-%281%2Fm%29x%2Bk must contain the point (u,v), then you can use the coordinates
of this point to find k, the y-intercept for+y=-%281%2Fm%29x%2Bk. As before, now solve for k.
highlight_green%28k=y-%28-%281%2Fm%29%29x%29, the y-intercept for the line through (u,v) perpendicular to y=mx%2Bb.

Using the parts separately might be easier than trying to put all of this into a single formula.


SPECIFICALLY FOR YOUR EXAMPLE

Given highlight_green%28y=-2x-4%29 Find the line perpendicular to it which contains the point (1,0).
The slope of this perpendicular line is 1%2F2, and to find the y-intercept, you can start with
y=%281%2F2%29x%2Bk
y-%281%2F2%29x=k
k=y-%281%2F2%29x
Substitute the specific point to be passed-through
k=0-%281%2F2%29%2A1
k=-%281%2F2%29
The line wanted is highlight%28y=%281%2F2%29x-1%2F2%29