SOLUTION: Find the equation of the line (in slope-in form) that is perpendicular to 2x-y=4 and passes through the vertex of the parabola y=x^2-6x+7 I know slope int for is 2x-4=y but havin

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line (in slope-in form) that is perpendicular to 2x-y=4 and passes through the vertex of the parabola y=x^2-6x+7 I know slope int for is 2x-4=y but havin      Log On


   

Question 442168: Find the equation of the line (in slope-in form) that is perpendicular to 2x-y=4 and passes through the vertex of the parabola y=x^2-6x+7
I know slope int for is 2x-4=y but having problems with the rest
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general form
+y+=+m%2Ax+%2B+b+ where +m+ = slope
given:
y+=+2x+-+4+
The slope of a line perpendicular to this line
has slope = +-1%2F2+
So far,
+y+=+%28-1%2F2%29%2Ax+%2B+b+
The vertex of +y+=+x%5E2+-+6x+%2B+7+
is at ( -b/(2a) , y ) where
+a+=+1+
+b+=+-6+
++-%28-6%29+%2F+%282%2A1%29+=+3+
To find the y coordinate
+y+=+x%5E2+-+6x+%2B+7+
+y+=+3%5E2+-+6%2A3+%2B+7+
+y+=+9+-+18+%2B+7+
+y+=+-2+
Go back to:
+y+=+%28-1%2F2%29%2Ax+%2B+b+
+-2+=+%28-1%2F2%29%2A3+%2B+b+
+-2+=+-3%2F2+%2B+b+
+2b+=+-4+%2B+3+
+b+=+-1%2F2+
------------
+y+=+%28-1%2F2%29%2Ax+-+1%2F2+ answer
Here's the plot: