Answer:
[tex]8x-y=73[/tex]
Step-by-step explanation:
[tex]\text{Solution:}\\\text{Let the slope of the line }y=-\dfrac{x}{8}-6\text{ be }m_1\text{ and the slope of the line}\\\text{perpendicular to this line be }m_2.[/tex]
[tex]\text{Then, comparing }y=-\dfrac{x}{8}-6\text{ with }y=m_1x+c,\ \text{slope }(m_1)=-\dfrac{1}{8}\\\\\text{Using the condition of perpendicular lines,}\\m_1.m_2=-1\\\\\text{or, }-\dfrac{1}{8}.m_2=-1\\\\\text{or, }m_2=8[/tex]
[tex]\text{The line with slope }m_2\text{ passes through the point (8,-9). So it's equation will be:}\\y-(-9)=m_2(x-8)\\\text{or, }y+9=8(x-8)\\\text{or, }y+9=8x-64\\\text{or, }8x-y=73\text{ is the required equation.}[/tex]
