Question 910598
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
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