SOLUTION: I need help with this problem can someone please help !! Write the equation of a line that is perpendicular to the given line and that passes through the given point y-3= -1/

Algebra ->  Linear-equations -> SOLUTION: I need help with this problem can someone please help !! Write the equation of a line that is perpendicular to the given line and that passes through the given point y-3= -1/      Log On


   

Question 1037043: I need help with this problem can someone please help !!
Write the equation of a line that is perpendicular to the given line and that passes through the given point
y-3= -1/5x (+2); (-2,7)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you are given a line with slope = +m%5B1%5D+,
then ANY line perpendicular to the given line
will have slope = +m%5B2%5D+=+-1%2Fm%5B1%5D+
-------------------------------------
You are given:
+y+-+3+=+-%281%2F5%29%2Ax+%2B+2+ ( is this it? Is there a typo? )
+y+=+-%281%2F5%29%2Ax+%2B+5+
The slope is: +m%5B1%5D+=+-%281%2F5%29+
Any line perpendicular to this line has slope:
+m%5B2%5D+=+-1+%2F+%28+-%281%2F5%29+%29+
+m%5B2%5D+=+5+
-----------------
The line you are looking for passes through (-2,7 )
Use the general point-slope formula:
+%28+y+-+7+%29+%2F+%28+x+-+%28-2%29+%29+=+5+
+y+-+7+=+5%2A%28+x+%2B+2+%29+
+y+-+7+=+5x+%2B+10+
+y+=+5x+%2B+17+ answer
----------------------
check:
does the line go through (-2,7) ?
+y+=+5x+%2B+17+
+7+=+5%2A%28-2%29+%2B+17+
+7+=+-10+%2B+17+
+7+=+7+
OK
Here is a plot of the 2 lines:
+graph%28+500%2C+500%2C+-26%2C+26%2C+-24%2C+24%2C+-%281%2F5%29%2Ax+%2B+5%2C+5x+%2B+17+%29+