Question 15290
First find the slope of the given line:

{{{m= (y[2]-y[1])/( x[2] - x[1])}}}
 
{{{m= (7-(-3))/(2-1) = 10/1 = 10}}}


The slope of a line perpendicular to this line is tne negative reciprocal of the slope of this line.  So, the slope of a line perpendicular to this line has a slope of {{{(-1)/10}}}.


The equation of a line that is perpendicular to the line between these two points will be in the form {{{y = (-1/10)x+b}}} where b is the y-intercept of the line.  Notice that there are many, many (in fact, infinitely many) lines that are perpendicular to this line segment, and to determine which particular line you are looking for, more information must be given in the problem.


Final answer, {{{y = (-1/10)x+b}}} .


R^2 at SCC