Question 122776
First lets find the slope through the points ({{{5}}},{{{1}}}) and ({{{-2}}},{{{7}}})


{{{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 ({{{5}}},{{{1}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{-2}}},{{{7}}}))


{{{m=(7-1)/(-2-5)}}} Plug in {{{y[2]=7}}},{{{y[1]=1}}},{{{x[2]=-2}}},{{{x[1]=5}}}  (these are the coordinates of given points)


{{{m= 6/-7}}} Subtract the terms in the numerator {{{7-1}}} to get {{{6}}}.  Subtract the terms in the denominator {{{-2-5}}} to get {{{-7}}}

  


{{{m=-6/7}}} Reduce

  

So the slope is

{{{m=-6/7}}}


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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=(-6/7)(x-5)}}} Plug in {{{m=-6/7}}}, {{{x[1]=5}}}, and {{{y[1]=1}}} (these values are given)



{{{y-1=(-6/7)x+(-6/7)(-5)}}} Distribute {{{-6/7}}}


{{{y-1=(-6/7)x+30/7}}} Multiply {{{-6/7}}} and {{{-5}}} to get {{{30/7}}}


{{{y=(-6/7)x+30/7+1}}} Add {{{1}}} to  both sides to isolate y


{{{y=(-6/7)x+37/7}}} Combine like terms {{{30/7}}} and {{{1}}} to get {{{37/7}}} (note: if you need help with combining fractions, check out this <a href=http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver>solver</a>)




{{{7y=-6x+37}}} Multiply both sides by 7 to clear the fractions



{{{6x+7y=37}}} Add 6x to both sides