SOLUTION: What is the slope-intercept form of a line passing through (-3, -5) that is perpendicular to the line x + 3y = 6? not sure what I am doing wrong it is not working for me thank

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Question 545001: What is the slope-intercept form of a line passing through (-3, -5) that is perpendicular to the line x + 3y = 6?
not sure what I am doing wrong it is not working for me thanks bunches
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
What is the slope-intercept form of a line passing through (-3, -5) that is perpendicular to the line x + 3y = 6?
The given line has intercepts (0,2) and (6,0) 
Here is the given line and the given point:

 

First we find the slope of the given line by getting it into the
slope-intercept form y = mx+b

x + 3y = 6
    3y = -x + 6
    3y = -1x + 6
    3%2F3y = %28-1%29%2F3%29%29%29x+%2B+%28%28%286%2F3

     y = -1%2F3x + 2

Compare that to

     y = mx + b

and the slope of the given line is m = -1%2F3.

Since the required line is to be perpendicular to the
given line, its slope is found by inverting the given
line's slope and giving it the opposite sign. Inverting
and changing the sign of -1%2F3 gives %22%22%2B3%2F1, or just 3.

Then we use the point-slope form:

y - y1 = m(x - x1)

with m = 3, (x1,y1) = (-3,-5).

y - (-5) = m[x - (-3)]

   y + 5 = 3(x + 3)

   y + 5 = 3x + 9
   
       y = 3x + 4

That's the required line.  Let's graph it as a check.
It has intercepts (0,4) and (-4%2F3,0), which is (-1%261%2F3,0), 
Let's draw it in green:


  
The green line whose equation we found sure looks perpendicular 
to the black one, whose equation was given, so it must be correct.

Answer:        y = 3x + 4

Edwin