How do you write an equation of the line perpendicular to 3x+y-6=0 and passing through point P(5,2)?

Question

please help me thank-you:D

Answer 1

First find the slope of the given line.
To find the slope, solve for y
Subtract 3x from each side and add 6 to each side
y = -3x + 6
The slope of this line is -3.
The slope of a line that is perpendicular to the given line is the negative reciprocal of -3, which is 1/3
Use the formula y = mx+b
Plug in m = 1/3, x = 5 and y = 2, then solve for b.
2 = (1/3)(5) + b
2 = 5/3 + b
Subtract 5/3 from each side and get a common denominator
6/3 - 5/3 = b
1/3 = b
Answer: y = (1/3)x + 1/3

Answer 2

rearrange the equation of the given line into y=mx+b form so you can identify the slope (m)
the slope of the perpendicular line will be -1/m,
the negative reciprocal of the slope of the first line

now you have the slope and a point on the line
use the point-slope form of the equation of a line
y - Y = m(x-X)
where the capital X and Y are the coordinates of the given point

the power of algebra is that once you've solved this type of problem once, you can solve it for the general case, and then you don't have to go through all the tedious steps

given Ax + By + C = 0 and the point (u, v):
the perpendicular line is
y = (B/A)x + [v - (B/A)u]

you were given A=3, B=1, C=-6, u=5, v=2
y = x/3 + (2- 5/3) = x/3 +1/3

Answer 3

it is usually easier to first put the equation of the line in slope intercept form

3x+y-6=0

y=-3x+6

the slope of this line is therefore "-3"

the perpendicular line, will have to have slow 1/3 (if you think about it you can see that the perpendicular line to the line with slope "m" will have slope "-1/m")

so, the line you are looking for has slope 1/3 and goes through the point (5,2)

the general equation for a line in slope intercept form is:

y=mx+b

your equation has slope (m) =1/3, and the pair (5,2) is a point on the line so when x=5, then y=2 so we can substitute those values

2=1/3(5)+b

solve for b

2=5/3+b
6/3=5/3+b
1/3=b

so, the equation is y=1/3x+1/3

you better check my math and arithmetic because I could have easily made an error, but hopefully you can see how to work through a problem of this kind

good luck

Answer 4

Hey Mitsuki!

you would first re-arrange the question so it's in the y=mx+b format.

That would be y=-3x+6

Then you would solve it like any other equation of this category.

Use the formula y-y1=m(x-x1)

Change the slope of the equation to a negative reciprocal. In this case, it would be 1/3

Then substitute the values in. m would be the slope, x1 would be 5 (from [5,2]) and y1 would be 2.

Simply solve the equation..

Here:
y-y1=m(x-x1)
y-2=1/3(x-5)
y=1/3x-1 2/3 +2

y=1/3x +1/3

So basically the answer would be y=1/3x +1/3. Hope that helped! ^_^

Answer 5

slope of the given line=-3
slope of the required line=1/3
passing through(5,2)
y-y1=m(x-x1)
y-2=1/3(x-5)
3y-6=x-5
x-3y+1=0 is the required equation