1. ## write the gradient of the line perpendicular to...?

hi,

i need to know how to write the gradient of the line perpendicular to Y=3x+1.

i don't really know how to do this and some help would be great!!!

thanks!

p.s. sorry if topic is in wrong place, wasn't sure where to post.

2. ## Re: write the gradient of the line perpendicular to...?

Originally Posted by andyboy179
i need to know how to write the gradient of the line perpendicular to Y=3x+1.
Given the line $\displaystyle y=mx+b,~m\ne 0$ then the line $\displaystyle y=\frac{-1}{m}x+c$ is perpendicular to the given line.

3. ## Re: write the gradient of the line perpendicular to...?

i don't understand hot you got y=-1/mx+c. is that the gradient?

4. ## Re: write the gradient of the line perpendicular to...?

the gradient of this is 3/1 =3
so to get the perpendicular gradient would i swap them around and swap the sign on top?
so i would have -1/3=-0.3??

5. ## Re: write the gradient of the line perpendicular to...?

If m is the gradient of the line y=mx+c than 1/m is the gradient of the line: y=-1/mx+C perpendicular to y=mx+c.
And also: $\displaystyle m\cdot \frac{-1}{m}=-1$.

6. ## Re: write the gradient of the line perpendicular to...?

Okay. Can we go through this one step at a time?

2. If so is the gradient of the line perpendicular to Y=3x+1 =-3/1?

3. Again, if so would the final answer be Y=-3/1x+1?

If this is not correct can you point out which step of what i have said is wrong please.

7. ## Re: write the gradient of the line perpendicular to...?

Originally Posted by andyboy179
write the gradient of the line perpendicular to $\displaystyle y=3x+1$.
The gradient of the line perpendicular to $\displaystyle y=3x+1$ is $\displaystyle ~~\frac{-1}{3}$

8. ## Re: write the gradient of the line perpendicular to...?

oh i thought you swap them around and swap the sign on the top one. Thanks!!

would i just write -1/3 for the answer or would i need to put it in form of Y=mx+c?

9. ## Re: write the gradient of the line perpendicular to...?

It depends, if they just ask to give the gradient it satisfies to write: -1/3.
If they ask to find the equation of the straight line with the gradient -1/3 you have to write it in the form:
y=mx+c

10. ## Re: write the gradient of the line perpendicular to...?

mine is in form of y=mx+c, so i would put y=-1/3x+1?

11. ## Re: write the gradient of the line perpendicular to...?

also can the perendicular gradient denominator be a minus?

12. ## Re: write the gradient of the line perpendicular to...?

Originally Posted by andyboy179
also can the perendicular gradient denominator be a minus?
All three of these forms are the equal.
$\displaystyle -\frac{1}{3}=\frac{-1}{3}=\frac{1}{-3}$.

The first two are preferred.

13. ## Re: write the gradient of the line perpendicular to...?

Originally Posted by Plato
All three of these forms are the equal.
$\displaystyle -\frac{1}{3}=\frac{-1}{3}=\frac{1}{-3}$.

The first two are preferred.
ok thank, i was just curious, however back to my question would the final answer be y=-1/3x+1?

14. ## Re: write the gradient of the line perpendicular to...?

You have the equation of the (given) line:
y=3x+1
And now you've found the gradient of a line perpendicular to y as you know.
In y the 1 is the point at which the line y crosses the y-axis, this hasn't to be the same for the line perpendicular to y, you've a lot of options. You only have the choose one.
(You only have one option when they ask to give the equation of the line perpendicular to y and going through a given point)

So maybe it's a little bit confusing but draw y=3x+1, now draw a line perpendicular to y and look where that line crosses the y-axis so you can create the equation of the line perpendicular to y.

Is that clear or? ...

15. ## Re: write the gradient of the line perpendicular to...?

mine crossed the y axis at 1? is that okay

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