Write the equation of a line perpendicular to the given line but passing through the given point. y = -3x-6 (-1, 5)

Question

I need to use the slope intercept form which is y –y1 = m (x – x1)

Answer 1

y = mx + b   is slope-intercept form of the linear equation.

y - y₁ = m(x - x₁)   is point-slope form of the linear equation.

Ax + By = C  (A ≥ 0)   is standard form of the linear equation.
~~~~~~~~~~~
....
               1 
y – 5  =  ——  (x + 1)
               3 
          1             1
y  =  —— x  +  ——  +  5
          3             3 

                    1             16
 (1)   y  =  ——  x  +  ——
                   3              3  

Or

        3y = x + 16 
      - x + 3y = 16
(2)    x - 3y = - 16  

If there is no any specific request, the answer should be in one out of two forms
  (1)  slope-intercept form
or
  (2)  standard form

Answer 2

y = -3x-6

comparing the above line in the form:

y  = mx +c

m = -3

The equation of the line perpendicular to the above line  will have the slope m = 1/3 ( opposite reciprocal)

so the equation of the line passing through ( -1, 5) using the slope intercept form  y –y1 = m (x – x1) =

y-5 = 1/3 ( x+1)

3y - 15 = x + 1

x - 3y + 16 = 0