Question

What is the equation of the line passing through (8, –6) and perpendicular to the line y = x – 2 in slope-intercept form?

Can someone please walk me through it? I really need to understand how to do this.

Answer 1

I know how to write an equation of a line, but how do I make it perpendicular to another line?

Answer 2

Well, if it's perpendicular (and parallel) are ALL ABOUT SLOPES :)
Parallel lines have the same slope, while perpendicular lines have slopes which are negative reciprocals of each other :)
What's the slope of
y = x - 2
?

Answer 3

1 right?

Answer 4

Right :)
so the slope of the line you want to construct must be the negative of the reciprocal of 1, which is...?

Answer 5

-1

Answer 6

but why would it be changed to the negative reciprocal?

Answer 7

I'm not really sure how to answer that :(
I guess it just is :)

Answer 8

Lol so if I have a slope of one and I am trying to do this type of question it is just the negative reciprocal?

Answer 9

Well, it's the negative reciprocal because this new line you want is perpendicular to the given line :)

Answer 10

Okay! Thanks! So what's next

Answer 11

Well, you now have your slope, and a point. You know how to construct the line, given a point and a slope?

Answer 12

Wait so my slope is -1 correct? And which point are we talking about now? The y-int or (8, -6) ?

Answer 13

The point (8,-6), of course :)

Answer 14

So then the y intercept would be positive 2 right?

Answer 15

Hmm...
given the slope m
and a point (a ,b) on the line, the equation of the line is given by
y - b = m(x - a)
You have m = -1
(a,b) = (8, -6)
Just plug in :)

Answer 16

Ohhh okay! thank you so much!

Answer 17

No problem :)