Perpendicular lines have slopes that are negative reciprocals. First, we write the given equation in slope intercept form by solving for y:

x−y=5

x−5=y

or

y=x-5

So, the slope of the given line is 1 which means that the slope of the line perpendicular to it is:

\(\displaystyle-{\left(\frac{{1}}{{1}}\right)}=-{1}\)

x−y=5

x−5=y

or

y=x-5

So, the slope of the given line is 1 which means that the slope of the line perpendicular to it is:

\(\displaystyle-{\left(\frac{{1}}{{1}}\right)}=-{1}\)