Find an equation of the line that satisfies the given conditions. Through (−8, −8); perpendicular to the line passing through (−5, 4) and

Let the line passing(-8,-8) be L1 and another one be L2

 

Slope of L2 : $${\frac{\left({\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{\left({\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}}$$=$${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

Since L1 perpendicular to L2

Slope of L1 x Slope of L2 = -1

Slope of L1 x $${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ = -1

Slope of L1 = 2

 

Equation of L1 : $${\frac{\left({\mathtt{y}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}\right)}}$$=2

y+8=2x+16

2x-y+8=0

Therefore, equation of the line passing through (-8,-8) is 2x-y+8=0