What is the equation of the line perpendicular to #y=-5/8x # that passes through # (-6,3) #?
Consider the standard equation form of a strait line graph:
A straight line that is perpendicular to this will have the gradient:
The equation perpendicular to this will be
We know it passes through the point
Substitute this point into equation (2) giving:
So equation (2) becomes:
I opted for fractional form for consistency of format. This is because the 5 in
Therefore slope of the given line is
If two lines are perpendicular then the product of their slopes is
Let the slope of the line perpendicular to the given line be
Then by definition
This is the slope of required line and the line required line also passes through
Using point slope form
This is the required line.