find the slope of any line perpendicular to the line through (5,3) and (2,5)

For this case we have that the slope of a line is given by:[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]Where:[tex](x_ {1}, y_ {1})[/tex] and[tex](x_ {2}, y_ {2})[/tex] are two points through which the line passes.According to the statement we have to:[tex](x_ {1}, y_ {1}) :( 2,5)\\(x_ {2}, y_ {2}): (5,3)[/tex]Then, the slope of the line is:[tex]m = \frac {3-5} {5-2} = \frac {-2} {3} = - \frac {2} {3}[/tex]By definition, if two lines are perpendicular then the product of their slopes is -1, that is:[tex]m_ {1} * m_ {2} = - 1[/tex]We find [tex]m_ {2}:[/tex][tex]m_ {2} = \frac {-1} {- \frac {2} {3}}\\m_ {2} = \frac {3} {2}[/tex]Answer:The slope of a perpendicular line is:[tex]m_ {2} = \frac {3} {2}[/tex]