Answer:
[tex]\large\boxed{y=-x-2}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of the equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\ \text{then}\\\\l\ ||\ k\iff m_2=m_1\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\========================\\\\\text{We have}\ k:y=x-2\to m_1=1\\\text{Therefore}\ m_2=-\dfrac{1}{1}=-1.\\\\l:y=-1x+b\to y=-x+b\\\\\text{Put the coordinates of the given point (-12, 10) to the equation:}\\\\10=-(-12)+b\\10=12+b\qquad\text{subtract 12 from both sides}\\-2=b\to b=-2\\\\\text{finally we have:}\\\\y=-x-2[/tex]
