Question 960330
First find the equation of the line through the two points.
Find the slope,
{{{m=(-2-4)/(1-(-5))=-6/6=-1}}}
{{{y-4=-1(x-(-5))}}}
{{{y-4=-(x+5)}}}
{{{y-4=-x-5}}}
{{{y=-x-1}}}
Perpendicular lines have slopes that are negative reciprocals.
{{{m[p]=-(1/(-1))=1}}}
{{{y-y[0]=1(x-x[0])}}}
{{{y-y[0]=x-x[0]}}}
Where {{{x[0]}}},{{{y[0]}}} is a point on the original line.
You can simplify since you know the equation of the original line.
{{{y-(-x[0]-1)=x-x[0]}}}
{{{y+x[0]+1=x-x[0]}}}
{{{y+1=x-2x[0]}}}
So now for any value of {{{x[0]}}}, you know the equation of the perpendicular line.