SOLUTION: Please help me solve this equation: What is the standard form of the equation of the line that is perpendicular to 6x+5y=9 and contains (-6,-1)

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Question 511583: Please help me solve this equation:
What is the standard form of the equation of the line that is perpendicular to 6x+5y=9 and contains (-6,-1)
Answer by Maths68(1474) (Show Source):
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Standard Form of Equation of the line:
y=mx+b
Given
6x+5y=9
rearrage the above equation according to the standard form
5y=-6x+9
5y/5=(-6x+9)/5
y=(-6/5)x+9/5
Compare above equation with the standard form equation
m=-6/5 and b=9/5
Since lines are perpendicular multiplicatin of their slope will be (-1)
So slope of the required line will be (5/6)
Now we have a point(-6,-1) and slope (5/6)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form.
m=(y2-y1)/(x2-x1)
5/6=(y-(-1))/(x-(-6))
5/6=(y+1)/(x+6)
5(x+6)=6(y+1)
5x+30=6y+6
-6y=6-5x-30
-6y=-5x-24
-6y/-6=(-5x+24)/-6
y=(-5/-6)x+(-24/-6)
y=(5/6)x+4
The standard form of the equation of the line
y=(5/6)x+4
that is perpendicular to 6x+5y=9 and contains (-6,-1)