SOLUTION: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused. Here is the equation y=-2x-1 (2,6)

Algebra ->  Graphs -> SOLUTION: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused. Here is the equation y=-2x-1 (2,6)      Log On


   

Question 122319: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused.
Here is the equation
y=-2x-1 (2,6)
Here is what I have
y=mx+b
6=-2(2)+b
6=-4+b
6+4=-4+b+4
10=b
y=1/2x+10
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of -2, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%28-2%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-2%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=1%2F2 Multiply the fractions.


So the perpendicular slope is 1%2F2



So now we know the slope of the unknown line is 1%2F2 (its the negative reciprocal of -2 from the line y=-2%2Ax-1). Also since the unknown line goes through (2,6), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-6=%281%2F2%29%2A%28x-2%29 Plug in m=1%2F2, x%5B1%5D=2, and y%5B1%5D=6



y-6=%281%2F2%29%2Ax-%281%2F2%29%282%29 Distribute 1%2F2



y-6=%281%2F2%29%2Ax-2%2F2 Multiply



y=%281%2F2%29%2Ax-2%2F2%2B6Add 6 to both sides to isolate y

y=%281%2F2%29%2Ax-2%2F2%2B12%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax%2B10%2F2 Combine the fractions



y=%281%2F2%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=-2%2Ax-1 and goes through (2,6) is y=%281%2F2%29%2Ax%2B5


So here are the graphs of the equations y=-2%2Ax-1 and y=%281%2F2%29%2Ax%2B5




graph of the given equation y=-2%2Ax-1 (red) and graph of the line y=%281%2F2%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (2,6)

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=-2X-1 (RED LINE)FOR A LINE TO BE PERPENDICULAR IT HAS A SLOPE EQUAL TO THE NEGATIVE RECIPRICAL OF THIS SLOPE.
THUS THE SLOPE OF THE PERPENDICULAR LINE =1/2.
USING THE LINE FORMULA:
Y=mX+b & SUBSTITUTION THE SLOPE VALUE=1/2 & USING THE POINT VALUES (2,6) WE SOLVE FOR b.
6=1/2*2+b
6=-+B
b=6-1
b=5 FOR THE Y INTERCEPT.
THUS THE EQUATION IS:
Y=X/2+5 (GREEN LINE)
+graph%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2C+y+=+-2x+-1%2C+y+=+x%2F2+%2B5%29+ (graph 300x300 pixels, x from -6 to 6, y from -6 to 6, of TWO functions y = -2x -1 and y = x/2 +5).