Find the equation of a line?

Question

I need to find the quation of the a line that pases through point (-2,1) and is perpendicualr to line 3x-4y=5

Answer 1

First just list the given variables
Passes through (-2,1)
And perpendicular to 3x-4y=5 (if it is perpendicular and it intersects it forms a kind of 'x', so the most importent thing to do first is find the slope)

1) finding slope

3x-4y=5
a) Isolate Y
-4y=5-3x
y=3/4x-5/4

slope is 3/4 but it is perpendicular so it is compleatly the opposite from 3/4 so slope for perpendicular line is (-4/3)

2)finding equation of line
using this u can find the equation it passes through (-2,1) right?

so u will get this

-4*(x+2)=3(y-1)
solve it and get

-4x-8=3y-3
so the answer is
-4x-3y=5 or 4x+3y=-5

Answer 2

Ok, so first look at the equation for the line that is perpendicular to the one you're finding. You'll need to put it into slope-intercept form (y=mx+b), so that it is y=whatever.

When I did this, I got y = 3/4x -5/4.

Then, because your line is perpendicular to this, that means the slope of your line, the coefficient of the x-term, is the negative reciprocal of the slope of the given line. So that means your new slope is -4/3. This is your m-term, and the x and y are given, so all you need left is the b-term.

To get this final number, you plug in the point (-2, 1) and the slope (-4/3). The equation will look like this:

1 = -4/3(-2) + b

Then if you do the arithmetic, you should get b = -5/3. You then put that into the regular equation, so if I did all of the calculating right, it should look like this:

y = -4/3x - 5/3

If you're still having trouble, your teacher will probably be glad to help you, so I recommend talking to him or her. = )

Answer 3

The slope of the line 3x-4y=5 is 3/4 (take the coefficient of X over the coefficient of Y and then negate it)
The slope of the line perpendicular to that is the negative reciprocal. That means you flip the number then negate it.
So the slope of the line you're looking for is -4/3.
The equation is in the form of 4x + 3y = C
To find C, we plug in the point you were given (-2, 1)
4(-2) + 3(1) = C
-8 + 3 = C
-5 = C

So the equation of the line is 4x + 3y = -5

Answer 4

The equation of a line is y=mx+b where m is the slope and b is the y-intercept.

OK. if you 'solve' your equation for y, you get y=3/4x - 5/4.

So, to make one line perpendicular to another line, the slopes must be negative reciprocals of each other. Thus, the slope of your perpendicular line should be -4/3.

Your new line now looks like y=-4/3x+b. Since your teacher gave you the y-intercept (1), we can just plug that in and your problem is solved:

y=-4/3x +1

Answer 5

3x-4y=5 is the same as y=3/4x-1 1/4

There was something to do with the negative opposite, but I don't remember. It's been awhile since I've done this type of problem.

Answer 6

take the recipricle (sp?) of 3/4x which is the slope then plug it into : y-y1=m(x-x1) and if my math is right ends up being y= -4/3x - 2/3, check that as i did the math in my head.