Question 200776


First let's find the slope of the line through the points *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(5,-3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,-3\right)].



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(-3-3)/(5--5)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=3}}}, {{{x[2]=5}}}, and {{{x[1]=-5}}}



{{{m=(-6)/(5--5)}}} Subtract {{{3}}} from {{{-3}}} to get {{{-6}}}



{{{m=(-6)/(10)}}} Subtract {{{-5}}} from {{{5}}} to get {{{10}}}



{{{m=-3/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(5,-3\right)] is {{{m=-3/5}}}



Now let's use the point slope formula:



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



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



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



{{{y-3=(-3/5)x+(-3/5)(5)}}} Distribute



{{{y-3=(-3/5)x-3}}} Multiply



{{{y=(-3/5)x-3+3}}} Add 3 to both sides. 



{{{y=(-3/5)x+0}}} Combine like terms. 



{{{y=(-3/5)x}}} Remove the trailing zero



{{{y=(-3/5)x}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(5,-3\right)] is {{{y=(-3/5)x}}}



 Notice how the graph of {{{y=(-3/5)x}}} goes through the points *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(5,-3\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(-3/5)x),
 circle(-5,3,0.08),
 circle(-5,3,0.10),
 circle(-5,3,0.12),
 circle(5,-3,0.08),
 circle(5,-3,0.10),
 circle(5,-3,0.12)
 )}}} Graph of {{{y=(-3/5)x}}} through the points *[Tex \LARGE \left(-5,3\right)] and *[Tex \LARGE \left(5,-3\right)]