Answer:
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
    ..................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
