What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 ?

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

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

Where m is the slope of the line

∴

On Comparing we get

The Required line is Perpendicular to the above line.

So,

Product of slopes = - 1

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

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is