Answer:
[tex]\large\boxed{A)\ y=-2x+15}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_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}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(10,\ -5).[/tex]
[tex]\text{Put the coordinates of the point to the equation.}\ x=10,\ y=-5:\\\\-5=-2(10)+b\\\\-5=-20+b\qquad\text{add 20 to both sides}\\\\b=15[/tex]
