Question 388332
{{{-4x+5y=-23}}} Start with the given equation.



{{{5y=-23--4x}}} Add {{{4x}}} to both sides.



{{{5y=--4x-23}}} Rearrange the terms.



{{{y=(--4x-23)/(5)}}} Divide both sides by {{{5}}} to isolate y.



{{{y=((--4)/(5))x+(-23)/(5)}}} Break up the fraction.



{{{y=(4/5)x-23/5}}} Reduce.



We can see that the equation {{{y=(4/5)x-23/5}}} has a slope {{{m=4/5}}} and a y-intercept {{{b=-23/5}}}.



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



Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope {{{m=-5/4}}} and the coordinates of the given point *[Tex \LARGE \left\(-3,7\right\)].



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



{{{y-7=(-5/4)(x--3)}}} Plug in {{{m=-5/4}}}, {{{x[1]=-3}}}, and {{{y[1]=7}}}



{{{y-7=(-5/4)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{4(y-7)=-5(x+3)}}} Multiply both sides by 4



{{{4y-28=-5x-15}}} Distribute.



{{{4y-28+5x=-15}}} Add 5x to both sides.



{{{4y+5x=-15+28}}} Add 28 to both sides.



{{{4y+5x=13}}} Combine like terms.



{{{5x+4y=13}}} Rearrange the terms.



Note: if you multiply EVERY term of the last answer choice by -1, you'll get the last equation I've shown. So this means that the two equations are equivalent. 



So the answer choice is choice D), although it's a strange way to represent an answer. 



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Jim