Question 93772
First lets find the slope through the points ({{{-2}}},{{{5}}}) and ({{{3}}},{{{-1}}})


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


{{{m=(-1-5)/(3--2)}}} Plug in {{{y[2]=-1}}},{{{y[1]=5}}},{{{x[2]=3}}},{{{x[1]=-2}}}  (these are the coordinates of given points)


{{{m= -6/5}}} Subtract the terms in the numerator {{{-1-5}}} to get {{{-6}}}.  Subtract the terms in the denominator {{{3--2}}} to get {{{5}}}

  

So the slope is

{{{m=-6/5}}}


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



{{{y-5=(-6/5)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



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


{{{y-5=(-6/5)x-12/5}}} Multiply {{{-6/5}}} and {{{2}}} to get {{{-12/5}}}


{{{y=(-6/5)x-12/5+5}}} Add {{{5}}} to  both sides to isolate y


{{{y=(-6/5)x+13/5}}} Combine like terms {{{-12/5}}} and {{{5}}} to get {{{13/5}}} (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>)



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Answer:



So the equation of the line which goes through the points ({{{-2}}},{{{5}}}) and ({{{3}}},{{{-1}}})  is:{{{y=(-6/5)x+13/5}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-6/5}}} and the y-intercept is {{{b=13/5}}}


Notice if we graph the equation {{{y=(-6/5)x+13/5}}} and plot the points ({{{-2}}},{{{5}}}) and ({{{3}}},{{{-1}}}),  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, -8.5, 9.5, -7, 11,
graph(500, 500, -8.5, 9.5, -7, 11,(-6/5)x+13/5),
circle(-2,5,0.12),
circle(-2,5,0.12+0.03),
circle(3,-1,0.12),
circle(3,-1,0.12+0.03)
) }}} Graph of {{{y=(-6/5)x+13/5}}} through the points ({{{-2}}},{{{5}}}) and ({{{3}}},{{{-1}}})