Question 221407
We can see that the equation {{{y=-8x+9}}} has a slope {{{m=-8}}} and a y-intercept {{{b=9}}}.



Now to find the slope of the perpendicular line, simply flip the slope {{{m=-8}}} to get {{{m=-1/8}}}. Now change the sign to get {{{m=1/8}}}. So the perpendicular slope is {{{m=1/8}}}.



Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope {{{m=1/8}}} and the coordinates of the given point *[Tex \LARGE \left\(-16,6\right\)].



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y-6=(1/8)(x--16)}}} Plug in {{{m=1/8}}}, {{{x[1]=-16}}}, and {{{y[1]=6}}}



{{{y-6=(1/8)(x+16)}}} Rewrite {{{x--16}}} as {{{x+16}}}



{{{y-6=(1/8)x+(1/8)(16)}}} Distribute



{{{y-6=(1/8)x+2}}} Multiply



{{{y=(1/8)x+2+6}}} Add 6 to both sides. 



{{{y=(1/8)x+8}}} Combine like terms. 



So the equation of the line perpendicular to {{{y=-8x+9}}} that goes through the point *[Tex \LARGE \left\(-16,6\right\)] is {{{y=(1/8)x+8}}}.



Here's a graph to visually verify our answer:

{{{drawing(500, 500, -20, 2, -8, 12,
graph(500, 500, -20, 2, -8, 12,-8x+9,(1/8)x+8)
circle(-16,6,0.08),
circle(-16,6,0.10),
circle(-16,6,0.12))}}}


Graph of the original equation {{{y=-8x+9}}} (red) and the perpendicular line {{{y=(1/8)x+8}}} (green) through the point *[Tex \LARGE \left\(-16,6\right\)]. 


If you need more help or practice with this topic, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/equation-parallel-or-perpendicular.solver>solver</a>.