Question

What is the equation of the line perpendicular to y = -x + 3 through (-1,-2)

Answer 1

if a line has slope m, the line perpendicular to it will have a slope of -1/m (the negative reciprocal)

Answer 2

you can use point slope form to find the equation (y-y1)=m(x-x1)

Answer 3

So I re-write it as y = 1/m + 3 first, then write -2+2(1) = 1/x(-1+1(1))?

Answer 4

to use point slope for you need two things. One point, which you were given, and a slope. You know the new slope (which is usually called "m") you know how to get the slope of a perpendicular line by flipping the fraction upside down (taking the reciprocal) and flipping the sign(from positive to negative or negative to positive)

Answer 5

If I replaced all the x's, y's and the new slope, how could I solve for anything though? Sorry, this is the first time I've done this type of problem

Answer 6

Let me walk you through step by step:
What is the slope of y = -x + 3?

Answer 7

3

Answer 8

Sorry, meant -1

Answer 9

ok -1 is correct.

Answer 10

Wasn't thinking, sorry. so the new slope would be 1/x? that's the inverse reciprocal?

Answer 11

The slope of the perpendicular line will be the negative reciprocal of the previous slope:
that is -1/(previous slope)
So what is the slope of the perpendicular line?

Answer 12

-1/-1 = 1

Answer 13

correct.

Answer 14

The equation of a line is y = mx + b
You know the slope m to be 1.
So y = x + b
This line passes through the point (-1, -2). So put x = -1 and y = -2 in the above equation and solve for b.
b = ?

Answer 15

b = -1

Answer 16

Yes. Put b = -1 in the equation y = x + b and you now have the equation of the perpendicular line.

Answer 17

So the answer would be y = 1x -1

Answer 18

Yes. But no need to put the 1 in front of x because 1 multiplied by any number is the same number. So 1x = x.

Answer 19

Thank you so much, this has been very helpful! Really quick, I had another one of these problems with a perpendicular line and wanted to check if it was correct. It was perp to 5x + 3y = 1 and the answer was y = 3/5x +5

Answer 20

You have to give me the point the perpendicular passes through.

Answer 21

Oh, I'm sorry. It was (-5,2)

Answer 22

y = 3/5x + 5
You have the correct answer!

Answer 23

Thank you! I will use your method to solve future problems like this one, the other one confused me a lot. But thank you again for your help!

Answer 24

You are very welcome!