# Thread: Find equation of a line perpendicular to something passing through something and some

1. ## Find equation of a line perpendicular to something passing through something and some

Find equation of a line perpendicular to something passing through something and something?
Please answer without the point slope formula I prefer the substitution method. I know how to find the equation of a line perpendicular to something passing through a given co ord but not something passing through 2 given co ords. Thanks, need this for my GCSE.

2. ## Re: Find equation of a line perpendicular to something passing through something and

Sorry, but this is a bit confused. Perhaps if you define what you mean by all those "somethings" it would be clearer what you're asking. Are you asking about lines perpendicular to lines, or perpendicular to circles, or 3-dimensional surfaces, or what? By "point slope method" are you talking about how to find the equation of a line given two sets of coordinates? Finally what do you mean by finding a line perpendicular to "something ...passing through 2 given coordinates?" Perhaps if you gave an example we could be of better help.

3. ## Re: Find equation of a line perpendicular to something passing through something and

Perpendicular to a given line.
Yes, I am.
Something 1 = equation of line
Something 2&3 = set of coords

find the equation of a line perpendicular to something 1 passing through something 2 and something 3

4. ## Re: Find equation of a line perpendicular to something passing through something and

It makes no sense to say that a line "passes through" a set of coordinates. Passing through the x and y axes at given points? There exist a unique line passing through given point perpendicular to a given line. Is that what you mean? PLEASE tell us exactly what the problem you are trying to solve is.

5. ## Re: Find equation of a line perpendicular to something passing through something and

Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)

That is an example.

6. ## Re: Find equation of a line perpendicular to something passing through something and

Originally Posted by Ashir
Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)

That is an example.
that would be two lines ... both perpendicular to y = 4x+2 , one passing through (3,-5) and the other passing through (4,8)

perpendicular slope is the opposite reciprocal of the slope of the given line ... use the point-slope form of a linear equation to find each line's equation.

7. ## Re: Find equation of a line perpendicular to something passing through something and

that was just an example, switch 4,8 with 2, -4 then so it's one line

I'm not comfortable with the pointslope formula but with substituting.

8. ## Re: Find equation of a line perpendicular to something passing through something and

Originally Posted by Ashir
Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)

That is an example.
This is impossible as written. You can find a line that is perpendicular to y=4x+2 that passes through (3,-5), or you can find a line that is perpendicular to y=4x+2 that passes through (4,8), but there is no single line that is perpendicular to y=4x+2 and that passes through BOTH (3,-5) and (4,8).

9. ## Re: Find equation of a line perpendicular to something passing through something and

Originally Posted by Ashir
that was just an example, switch 4,8 with 2, -4 then so it's one line

I'm not comfortable with the pointslope formula but with substituting.
If you are given two points such as (3,-5) and (2, -4) you can find the equation of the line that includes both of these poimts using the formula:

$\displaystyle y=mx+b$ where m is the slope: $\displaystyle m=\frac {\Delta y}{\Delta x} = \frac {(y_2-y_1)}{(x_2-x_1)}$ and b (the y intercept) can be found from $\displaystyle y_1 = mx_1+b$. So here you have $\displaystyle y=\frac {-4- (-5)}{2-3} = -1$, and $\displaystyle -5=(-1)(3) + b$, so $\displaystyle b = -5+3 = -2.$ So the equation of the line passing through these two points is y=-x-2.

But this has nothing to do with a line being perpendicular to y = 4x+2, because it's not.