Question 117320
First lets find the slope through the points ({{{-3}}},{{{7}}}) and ({{{5}}},{{{-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 ({{{-3}}},{{{7}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{5}}},{{{-1}}}))

{{{m=(-1-7)/(5--3)}}} Plug in {{{y[2]=-1}}},{{{y[1]=7}}},{{{x[2]=5}}},{{{x[1]=-3}}}  (these are the coordinates of given points)

{{{m= -8/8}}} Subtract the terms in the numerator {{{-1-7}}} to get {{{-8}}}.  Subtract the terms in the denominator {{{5--3}}} to get {{{8}}}

{{{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-7=(-1)(x--3)}}} Plug in {{{m=-1}}}, {{{x[1]=-3}}}, and {{{y[1]=7}}} (these values are given)

{{{y-7=(-1)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}

{{{y-7=-x+(-1)(3)}}} Distribute {{{-1}}}

{{{y-7=-x-3}}} Multiply {{{-1}}} and {{{3}}} to get {{{-3}}}

{{{y=-x-3+7}}} Add {{{7}}} to  both sides to isolate y

{{{y=-x+4}}} Combine like terms {{{-3}}} and {{{7}}} to get {{{4}}}

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Answer:

So the equation of the line which goes through the points ({{{-3}}},{{{7}}}) and ({{{5}}},{{{-1}}})  is:{{{y=-x+4}}}

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=4}}}

Notice if we graph the equation {{{y=-x+4}}} and plot the points ({{{-3}}},{{{7}}}) and ({{{5}}},{{{-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, 10, -6, 12,
graph(500, 500, -8, 10, -6, 12,(-1)x+4),
circle(-3,7,0.12),
circle(-3,7,0.12+0.03),
circle(5,-1,0.12),
circle(5,-1,0.12+0.03)
) }}} Graph of {{{y=-x+4}}} through the points ({{{-3}}},{{{7}}}) and ({{{5}}},{{{-1}}})

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