Question 24572
First of all we need to find the slope of the first line;
m={{{(Y2-Y1)/(X2-X1)}}}
m={{{(-2-4)/(3-1)}}}
m={{{-6/2}}}
m=-3
Now the perpindicular line to this will have a slope that is the opposite reciprocal -3, {{{1/3}}}
SO the slope of the new line is;
{{{1/3}}}
Use the point-slope form to find the equation;
Y-Y1=m(X-X1)
y-(-5)={{{1/3}}}(x-3)
y+5={{{1/3}}}x-1
y={{{1/3}}}x-1-5
So the equation would be;
y={{{1/3}}}x-6
Hope you understand!
=)