Question

Which is the equation for the line perpendicular to y = –5/3 x + 11 1/3 and containing P(–2, 3)?

I have been trying really hard but I want to make sure I know how to do this right. Please explain the steps and their purposes thoroughly so I can understand it. Thanks

Answer 1

Perpendicular lines have slopes that are inverse of one another and with opposite signs.
If a line has a slope of m=-2 than a perpendicular line will have slope m=1/2
If a line has a slope of m=-3/4 than a perpendicular line will have slope m=4/3
If a line has a slope of m=6 than a perpendicular line will have slope m=-1/6

So, just find the slope of your line, using it, get the slope of the line that will be perpendicular and then just get the equation for a line that has that slope and passes through point (-2,3) using:
y-y1=m(x-x1)

Answer 2

Okay, so you are trying to find the positive form of the line since it is negative and it needs to be perpendicular?

Answer 3

and then plug in the slope through y2-y1=m(x2-x1) ?

Answer 4

Would you make 5/3 x positive and then 11 1/3 negative?

Answer 5

No. Only the slope goes through that change. The equation for the line will be entirely different.

Answer 6

You make -5/3 positive, then get the inverse, that's the slope of your perpendicular line.
m=+3/5
Then sub that into:
y-y1=m(x-x1) Sub (x1,y1) with the point you need your line to pass through.

Answer 7

In my textbook in every equation it shows that the product of each slope is -1
how does that play out when solving this problem or do I ignore that all together?
I'm sorry I am still confused on the process of the steps, can you show all the steps in order? Thanks so much for your time!

Answer 8

The product of the two slopes will be -1 because you are inverting and changing the sign.
The slope of your sign is -5/3 If you invert it and change the sign, you get +3/5. If you multiply those two, you get -1. Same thing.
Now that you have the slope of the perpendicular line, you substitute it and the point you want the line to pass through into this equation:
y-y1=m(x-x1)
So m=+3/5
(x1,y1)=(-2,3)
So the equation will be:
y-(+3)=+3/5(x-(-2))
Multiply out, solve for y and you will get the equation of the perpendicular line that you need.