Question 117247
First lets find the slope through the points ({{{-1}}},{{{1}}}) and ({{{5}}},{{{-5}}})


{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula (note: *[Tex \Large \left(x_{1},y_{1}\right)] is the first point ({{{-1}}},{{{1}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{5}}},{{{-5}}}))


{{{m=(-5-1)/(5--1)}}} Plug in {{{y[2]=-5}}},{{{y[1]=1}}},{{{x[2]=5}}},{{{x[1]=-1}}}  (these are the coordinates of given points)


{{{m= -6/6}}} Subtract the terms in the numerator {{{-5-1}}} to get {{{-6}}}.  Subtract the terms in the denominator {{{5--1}}} to get {{{6}}}

  


{{{m=-1}}} Reduce

  

So the slope is

{{{m=-1}}}


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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
{{{y-y[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(\textrm{x_{1},y_{1}}\right)] is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


{{{y-1=(-1)(x--1)}}} Plug in {{{m=-1}}}, {{{x[1]=-1}}}, and {{{y[1]=1}}} (these values are given)



{{{y-1=(-1)(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-1=-x+(-1)(1)}}} Distribute {{{-1}}}


{{{y-1=-x-1}}} Multiply {{{-1}}} and {{{1}}} to get {{{-1}}}


{{{y=-x-1+1}}} Add {{{1}}} to  both sides to isolate y


{{{y=-x+0}}} Combine like terms {{{-1}}} and {{{1}}} to get {{{0}}}


{{{y=-x}}} Remove the zero terms  

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Answer:



So the equation of the line which goes through the points ({{{-1}}},{{{1}}}) and ({{{5}}},{{{-5}}})  is: {{{y=-x}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-1}}} and the y-intercept is {{{b=0}}}


Notice if we graph the equation {{{y=-x}}} and plot the points ({{{-1}}},{{{1}}}) and ({{{5}}},{{{-5}}}),  we get this: (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{drawing(500, 500, -7, 11, -11, 7,
graph(500, 500, -7, 11, -11, 7,(-1)x+0),
circle(-1,1,0.12),
circle(-1,1,0.12+0.03),
circle(5,-5,0.12),
circle(5,-5,0.12+0.03)
) }}} Graph of {{{y=-x}}} through the points ({{{-1}}},{{{1}}}) and ({{{5}}},{{{-5}}})


Notice how the two points lie on the line. This graphically verifies our answer.