Question

Write the equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5). I got y=-2x-1 but I don't think its right

Answer 1

Okay. Tell me how you got your answer?

Answer 2

Do you know how to get the slope of your original equation?

Answer 3

yes I know how to get slope, I did 5y=x-10 then subtracted from x and 10 so for slope I got -2 then I plugged it into y-5=-2(x-2) then I added 5 to both sides and got y=2x-1

Answer 4

why did you subtract x AND 10? when they're on opposite sides of each other? You're supposed to get the x and y on opposite sides of each other and leave the constant there.

Answer 5

I don't know. I did that before and still got the wrong answer I've tried to solve this like 4 times and every time I get a different wrong answer

Answer 6

You came to this spot:\[5y=x-10\]which is on the right path. Now how do you get the "y" by itself so you can get the original equation into standard form

Answer 7

I subtract the 5 from both sides?

Answer 8

scratch the earlier equation. The right equation that you should have been at is this one:\[5y=(-x)-10\]

Answer 9

No. You don't subtract the 5 when it's multiplied to the "y". Since it's multiplied to the "y" how do you take it out? What's the opposite action of multiplication?

Answer 10

Divide right?

Answer 11

Yes!

Answer 12

ugh sorry that's what I ment im getting all mixed up

Answer 13

It's okay. Sometimes you just have to slow down and think of what you're doing.

Answer 14

Now. Divide 5 from both sides and tell me what you get

Answer 15

5y/5=(-x)-10/5 which is y=-x-2 ..I don't think I did that right

Answer 16

you also have to divide the (-x) by 5, so the equation you should have came to is this:
\[\frac{ -5y }{- 5 }=\frac{ (-x) }{- 5 }-\frac{ -10 }{ -5 }\](My earlier equation had an error, it was a negative 5 times "y" not "5y" but "-5y")

you should have arrived at this spot:\[y=\frac{ x }{ 5 }+2\]

Answer 17

Can you understand how I got there?

Answer 18

Yeah I understand that, I didn't divide everything by the 5 but that's not the final answer is it?

Answer 19

No. It seems like I keep misplacing negatives here and there. I'll be more careful from now on so you'll get on the right path.

Now. Look at that last equation. What's the slope of that equation?

Answer 20

x/5 right?

Answer 21

so 5?

Answer 22

Yes. It's the constant times "x", where the constant 1/5 is our slope.

Answer 23

we could look at it like this, we know "x" is a slope of 1 over 1 right? but when we divide by "5" it's this\[\frac{ 1 }{ 5 }x\]right? it's the same thing.

Answer 24

oh okay yes I understand that

Answer 25

Since we're trying to find the equation of a line that is perpendicular to that line what do we need to do to the slope?

Answer 26

Plug it into the other formula? the y-y=m(x-x) one?

Answer 27

No. Then your equation will be PARALLEL since they have the SAME slope.

Answer 28

We want a PERPENDICULAR slope.

Answer 29

What we need to do is reverse the numerator and denominator of the slope of the original equation and times it by a negative.

Answer 30

May you please do that for me now and show me what you got.

Answer 31

yes hold on a sec

Answer 32

so y=5/x+2 then how do I times be a negative?

Answer 33

we only want to times the slope by a negative not the whole equation. So what I mean is this, here is your original slope:\[\frac{ 1 }{ 5 }x\]we flip the numerator and denominator\[\frac{ 5 }{ 1 }x\]then times it by a negative\[(-1)\frac{ 5 }{ 1 }x\]in the end it will look like this\[-5x\]

Answer 34

Understanding so far?

Answer 35

yes im sorry, no ones really ever teached me how to do this before

Answer 36

It's okay. This is why we're going step by step, so once you encounter this again. You'll know what to do.

Alright! Now we have the slope we need to plug into your equation:
\[(y-y _{2})=m(x-x _{2})\]Plug in your coordinates that it should pass and your new slope which cause it to be perpendicular. then display your answer

Answer 37

y-5=-5(x-5)
y-5=-5x-10
sub 5 so y=-5x+15 right?

Answer 38

I hope you meant y-5=-5(x-2) as your top equation. Becareful of your negatives. Recheck and do again.

Answer 39

You have the right answer. But your work leading to it is off. But in other words. Good job.

Answer 40

Oh okay well ill revise it but thank you so much for all the help, sorry it took so long

Answer 41

It's okay! Thank you for your diligence in working along. Good luck.