SOLUTION: How do I write one equation in slope-intercept form, and three other lines in slope-intercept form that are perpendicular to the first line?

Algebra ->  Linear-equations -> SOLUTION: How do I write one equation in slope-intercept form, and three other lines in slope-intercept form that are perpendicular to the first line?      Log On


   

Question 956732: How do I write one equation in slope-intercept form, and three other lines in slope-intercept form that are perpendicular to the first line?
Found 2 solutions by Fombitz, josmiceli:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Slope intercept form is,
y=mx%2Bb
A line perpendicular to that line would have a slope of,
m%5Bp%5D=-1%2Fm
since perpendicular lines have slopes that are negative reciprocals.
Then to get three lines that are perpendicular choose 3 different y-intercepts.
y=-%281%2Fm%29x%2Ba
y=-%281%2Fm%29x%2Bb
y=-%281%2Fm%29x%2Bc
where a%3C%3Eb%3C%3Ec
Example: Given y=2x%2B5, three perpendicular lines would be,
y=-x%2F2%2B1
y=-x%2F2%2B4
y=-x%2F2-3
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%2B5%2C-x%2F2%2B1%2C-x%2F2%2B4%2C-x%2F2-3%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the general form of one equation
looks like:
+y+=+m%2Ax+%2B+b%5B1%5D+,
then, for the other line to be perpendicular
to this one, the equation must look like:
+y+=+%28-1%2Fm%29%2Ax+%2B+b%5B2%5D+
--------------------------------------
+b%5B1%5D+ and +b%5B2%5D+ are y-intercepts
-----------------
For example:
For the 1st line:
+m+=+-1%2F2+
+b%5B1%5D+=+7+
-----------------
For the 2nd line:
+-1%2Fm+=+-1%2F%28-1%2F2%29+
+-1%2Fm+=+2+
+b%5B2%5D+=+1+
----------------------
Here's the lines:
+y+=+-%281%2F2%29%2Ax+%2B+7+
+y+=+2x+%2B+1+
-----------------------
Here are the plots:
+graph%28+600%2C+600%2C+-5%2C+18%2C+-5%2C+18%2C+-%281%2F2%29%2Ax+%2B+7%2C+2x+%2B+1+%29+