Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x-10}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the equation of a line in standard form}\ Ax+By=C.\\\text{Convert to the slope-intercept form}\ y=mx+b\\\\2x+y=-7\qquad\text{subtract 2x from both sides}\\\\y=-2x-7\to m_1=-2\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation}\ y=\dfrac{1}{2}x+b.[/tex]
[tex]\text{The line passes through the point (8, -6). Put the coordinates of this}\\\text{point to the equation and solve}\ b:\\\\-6=\dfrac{1}{2}(8)+b\\\\-6=4+b\qquad\text{subtract 4 from both sides}\\\\-10=b\to b=-10\\\\\text{Finally we have:}\ y=\dfrac{1}{2}x-10[/tex]
