SOLUTION: write an equation of perpendicular line through (1,-5) perpendicular to y=1/8x+2

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Question 910598: write an equation of perpendicular line through (1,-5) perpendicular to y=1/8x+2
Found 2 solutions by MathLover1, tutoringisfun:
Answer by MathLover1(20850) 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 1%2F8, 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%281%2F8%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%288%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-8%2F1 Multiply the fractions.


So the perpendicular slope is -8



So now we know the slope of the unknown line is -8 (its the negative reciprocal of 1%2F8 from the line y=%281%2F8%29%2Ax%2B2). Also since the unknown line goes through (1,-5), 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%2B5=-8%2A%28x-1%29 Plug in m=-8, x%5B1%5D=1, and y%5B1%5D=-5



y%2B5=-8%2Ax%2B%288%29%281%29 Distribute -8



y%2B5=-8%2Ax%2B8 Multiply



y=-8%2Ax%2B8-5Subtract -5 from both sides to isolate y

y=-8%2Ax%2B3 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F8%29%2Ax%2B2 and goes through (1,-5) is y=-8%2Ax%2B3


So here are the graphs of the equations y=%281%2F8%29%2Ax%2B2 and y=-8%2Ax%2B3




graph of the given equation y=%281%2F8%29%2Ax%2B2 (red) and graph of the line y=-8%2Ax%2B3(green) that is perpendicular to the given graph and goes through (1,-5)

Answer by tutoringisfun(17) About Me  (Show Source):
You can put this solution on YOUR website!
Good evening student. I hope that this is helpful to you.
to solve this problem it is important to remember that perpendicular lines have slopes that are the reciprocal of each other.
In order to find the equation of the desired line, we have to use the following formula
(y-y1)=m(x-x1)
Which is also known as the point slope form.
I will write the equation of the new line in the slope intercept form as given in the problem.

first we plug in our values for x1,y1 and m which are given in the problem as follows
x1=1, y1=-5, m= 8
m is 8 because that is the reciprocal of 1/8. As mentioned earlier, perpendicular lines have recirocal slopes.
When we plug the values into the above formula we get:
(y--5)=8(x-1)
since 2 negatives make a positive, we can rewrite the equation as:
y+5=8(x-1)

in order to get rid of the parenthesis we distribute the 8 which gives us
y+5=8x-8
we want to get y by itself, therefore we have to subtract 5 from each side
y+5-5=8x-8-5 the +5 and the -5 on the left cancel each other out leaving
y=8x-8-5
next we combine like terms to get:
y=8x-13
that is our answer.
If you would like more practice or need extra help converting from one formula to another check out my lesson http://www.algebra.com/my/change-this-name6828.lesson?content_action=show_dev I am also available for PAID assistance by contacting me on the following website:https://www.facebook.com/tutoringinquiry
or message me at www.instaedu.com