Answer:
y = -x + 3
Step-by-step explanation:
[tex]\text{Let:}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ ||\ l\iff m_1=m_2\\\\k \perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\==================================[/tex]
[tex]\text{We have the equation of a line}\\\\k:y=x-1\to m_1=1\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{1}=-1\\\\\text{Initially, our equation has the form}\\\\y=-1x+b\Rightarrow y=-x+b[/tex]
[tex]\text{The line should pass through point (5, -2).}\\\text{We substitute the coordinates of the point into the equation:}\\\\-2=-5+b\qquad\text{add 5 to both sides}\\\\-2+5=-5+5+b\\\\3=b\to b=3\\\\\text{Finally:}\\\\y=-x+3[/tex]
