Answer:
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
![6x+y=-5](https://tex.z-dn.net/?f=6x%2By%3D-5)
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( -2 , 7)
To Find:
Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?
Solution:
..................Given
which can be written as
![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
Where m is the slope of the line
∴ ![y=\dfrac{x}{6}-7](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bx%7D%7B6%7D-7)
On Comparing we get
![Slope = m = \dfrac{1}{6}](https://tex.z-dn.net/?f=Slope%20%3D%20m%20%3D%20%5Cdfrac%7B1%7D%7B6%7D)
The Required line is Perpendicular to the above line.
So,
Product of slopes = - 1
![m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6](https://tex.z-dn.net/?f=m%5Ctimes%20m_%7B1%7D%3D-1%5C%5CSubstituting%5C%20m%5C%5C%20%5Cdfrac%7B1%7D%7B6%7D%20m_%7B1%7D%3D-1%5C%5C%5C%5Cm_%7B1%7D%3D-6)
Slope of the required line is -6
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get
![(y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line](https://tex.z-dn.net/?f=%28y-7%29%3D-6%28x--2%29%3D-6%28x%2B2%29%3D-6x-12%5C%5C%5C%5C%5Ctherefore%206x%2By%3D-5.......is%5C%20the%20required%5C%20equation%5C%20of%5C%20the%5C%20line)
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
![6x+y=-5](https://tex.z-dn.net/?f=6x%2By%3D-5)