Question

What is an equation of the line that passes through the point ( − 6 , − 1 ) (−6,−1) and is perpendicular to the line 6 x − y = 7 6x−y=7?

Answer 1

Answer:

y =  $-\frac{1}{6}$ x - 2

Step-by-step explanation:

Given coordinate:

          ( − 6 , − 1 )

Equation of the given line is  6x− y = 7

Unknown:

Equation of the line that passes through the point and is perpendicular = ?

Solution:

A perpendicular line will have a slope that is of negative inverse to the one given;

              6x  - y  = 7

                     -y  = -6x  + 7

                     y  = 6x - 7

According to y= mx + c

 y and x are the coordinates

    m is the slope

     c is the y-intercept

Therefore, the slope of the line  = 6

  Perpendicular to this = $-\frac{1}{6}$

 The new line will be;

       Let find the intercept;

             -1  =  $-\frac{1}{6}$ x (-6) + c

             -1  = 1 + c

               c = -2

The new line is;

              y =  $-\frac{1}{6}$ x - 2