[tex]k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\Rightarrow m_2=-\dfrac{1}{m_1}[/tex]
We have:
[tex]k:y=\dfrac{1}{2}x+3;\ l:y=mx+b\\\\k\ \perp\ l\iff m=-\dfrac{1}{\frac{1}{2}}=-2\\\\therefore\ l:y=-2x+b.[/tex]
The line l passes throught the point (10;-5). Subtitute the value of coordinates to the equation:
[tex]-5=-2\cdot10+b\\\\-20+b=-5\ \ \ \ |add\ 20\ to\ both\ sides\\\\b=15[/tex]
Answer: y = -2x + 15.
