Question 140614
Do you want to find the equation through these points?



First lets find the slope through the points ({{{12}}},{{{5}}}) and ({{{-4}}},{{{1}}})


{{{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 ({{{12}}},{{{5}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{-4}}},{{{1}}}))


{{{m=(1-5)/(-4-12)}}} Plug in {{{y[2]=1}}},{{{y[1]=5}}},{{{x[2]=-4}}},{{{x[1]=12}}}  (these are the coordinates of given points)


{{{m= -4/-16}}} Subtract the terms in the numerator {{{1-5}}} to get {{{-4}}}.  Subtract the terms in the denominator {{{-4-12}}} to get {{{-16}}}

  


{{{m=1/4}}} Reduce

  

So the slope is

{{{m=1/4}}}


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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=(1/4)(x-12)}}} Plug in {{{m=1/4}}}, {{{x[1]=12}}}, and {{{y[1]=5}}} (these values are given)



{{{y-5=(1/4)x+(1/4)(-12)}}} Distribute {{{1/4}}}


{{{y-5=(1/4)x-3}}} Multiply {{{1/4}}} and {{{-12}}} to get {{{-12/4}}}. Now reduce {{{-12/4}}} to get {{{-3}}}


{{{y=(1/4)x-3+5}}} Add {{{5}}} to  both sides to isolate y


{{{y=(1/4)x+2}}} Combine like terms {{{-3}}} and {{{5}}} to get {{{2}}} 

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Answer:



So the equation of the line which goes through the points ({{{12}}},{{{5}}}) and ({{{-4}}},{{{1}}})  is:{{{y=(1/4)x+2}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=1/4}}} and the y-intercept is {{{b=2}}}


Notice if we graph the equation {{{y=(1/4)x+2}}} and plot the points ({{{12}}},{{{5}}}) and ({{{-4}}},{{{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, -5, 13, -6, 12,
graph(500, 500, -5, 13, -6, 12,(1/4)x+2),
circle(12,5,0.12),
circle(12,5,0.12+0.03),
circle(-4,1,0.12),
circle(-4,1,0.12+0.03)
) }}} Graph of {{{y=(1/4)x+2}}} through the points ({{{12}}},{{{5}}}) and ({{{-4}}},{{{1}}})


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