Respuesta :
First of all, to have two lines perpendiculars we need to remember that the multiplication of its slopes will be -1, we write this:
[tex]\text{slope 1 }\cdot\text{ slope 2=-1}[/tex]We deduce slope 1 from the given equation, comparing with a general form of the line, like this:
[tex]\begin{gathered} y=mx+b;\text{ m = slope; b = intercept with y axis} \\ y\text{ = -9x+17; from this comparation we deduce} \\ \text{slope 1=-9} \end{gathered}[/tex]Now we gonna find slope 2 throuht:
[tex]\begin{gathered} \text{slope 1 }\cdot\text{ slope 2 =-1} \\ -9\cdot\text{slope}2=-1 \\ \text{slope 2 =}\frac{\text{-1}}{-9} \\ \text{slope 2=}\frac{1}{9} \end{gathered}[/tex]finally, with that slope and the point (-8,4) we find a equation of a line, apply:
[tex]\begin{gathered} (y-y_1)=m(x-x_1);\text{ m=slope 2; (x}_1,y_1)=(-8,4) \\ y-4=\frac{1}{9}(x-(-8)) \\ y-4=\frac{1}{9}(x+8) \\ y=\frac{1}{9}x+\frac{8}{9}+4 \\ y=\frac{1}{9}x+\frac{44}{9} \end{gathered}[/tex]Finally, the equation for the line perpendicular to y=-9x+17 and contains the point (-8,4) is:
[tex]y=\frac{1}{9}x+\frac{44}{9}[/tex]