Question 336357
We can see that the equation {{{y=-(5/4)x+1}}} has a slope {{{m=-5/4}}} and a y-intercept {{{b=1}}}.



Now to find the slope of the perpendicular line, simply flip the slope {{{m=-5/4}}} to get {{{m=-4/5}}}. Now change the sign to get {{{m=4/5}}}. So the perpendicular slope is {{{m=4/5}}}.



Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope {{{m=4/5}}} and the coordinates of the given point *[Tex \LARGE \left\(2,6\right\)].



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



{{{y-6=(4/5)(x-2)}}} Plug in {{{m=4/5}}}, {{{x[1]=2}}}, and {{{y[1]=6}}}



{{{y-6=(4/5)x+(4/5)(-2)}}} Distribute



{{{y-6=(4/5)x-8/5}}} Multiply



{{{y=(4/5)x-8/5+6}}} Add 6 to both sides. 



{{{y=(4/5)x+22/5}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



So the equation of the line perpendicular to {{{y=-(5/4)x+1}}} that goes through the point *[Tex \LARGE \left\(2,6\right\)] is {{{y=(4/5)x+22/5}}}.



Here's a graph to visually verify our answer:

{{{drawing(500, 500, -10, 10, -10, 10,
graph(500, 500, -10, 10, -10, 10,-(5/4)x+1,(4/5)x+22/5)
circle(2,6,0.08),
circle(2,6,0.10),
circle(2,6,0.12))}}}


Graph of the original equation {{{y=-(5/4)x+1}}} (red) and the perpendicular line {{{y=(4/5)x+22/5}}} (green) through the point *[Tex \LARGE \left\(2,6\right\)]. 



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Jim