Question 115124
I'll do the first one to give you an idea how to do these types of problems 



First lets find the slope through the points ({{{5}}},{{{1}}}) and ({{{8}}},{{{-2}}})


{{{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 ({{{8}}},{{{-2}}}))


{{{m=(-2-1)/(8-5)}}} Plug in {{{y[2]=-2}}},{{{y[1]=1}}},{{{x[2]=8}}},{{{x[1]=5}}}  (these are the coordinates of given points)


{{{m= -3/3}}} Subtract the terms in the numerator {{{-2-1}}} to get {{{-3}}}.  Subtract the terms in the denominator {{{8-5}}} to get {{{3}}}

  


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



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


{{{y-1=-x+5}}} Multiply {{{-1}}} and {{{-5}}} to get {{{5}}}


{{{y=-x+5+1}}} Add {{{1}}} to  both sides to isolate y


{{{y=-x+6}}} Combine like terms {{{5}}} and {{{1}}} to get {{{6}}} 

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Answer:



So the equation of the line which goes through the points ({{{5}}},{{{1}}}) and ({{{8}}},{{{-2}}})  is:{{{y=-x+6}}}


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=6}}}


Notice if we graph the equation {{{y=-x+6}}} and plot the points ({{{5}}},{{{1}}}) and ({{{8}}},{{{-2}}}),  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, -2.5, 15.5, -9.5, 8.5,
graph(500, 500, -2.5, 15.5, -9.5, 8.5,(-1)x+6),
circle(5,1,0.12),
circle(5,1,0.12+0.03),
circle(8,-2,0.12),
circle(8,-2,0.12+0.03)
) }}} Graph of {{{y=-x+6}}} through the points ({{{5}}},{{{1}}}) and ({{{8}}},{{{-2}}})


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