Question 130381
First lets find the slope through the points ({{{3}}},{{{2}}}) and ({{{-2}}},{{{4}}})

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

{{{m=(4-2)/(-2-3)}}} Plug in {{{y[2]=4}}},{{{y[1]=2}}},{{{x[2]=-2}}},{{{x[1]=3}}}  (these are the coordinates of given points)

{{{m= 2/-5}}} Subtract the terms in the numerator {{{4-2}}} to get {{{2}}}.  Subtract the terms in the denominator {{{-2-3}}} to get {{{-5}}}

{{{m=-2/5}}} Reduce

So the slope is

{{{m=-2/5}}}

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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-2=(-2/5)(x-3)}}} Plug in {{{m=-2/5}}}, {{{x[1]=3}}}, and {{{y[1]=2}}} (these values are given)

{{{y-2=(-2/5)x+(-2/5)(-3)}}} Distribute {{{-2/5}}}

{{{y-2=(-2/5)x+6/5}}} Multiply {{{-2/5}}} and {{{-3}}} to get {{{6/5}}}

{{{y=(-2/5)x+6/5+2}}} Add {{{2}}} to  both sides to isolate y

{{{y=(-2/5)x+16/5}}} Combine like terms {{{6/5}}} and {{{2}}} to get {{{16/5}}} (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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So the equation of the line which goes through the points ({{{3}}},{{{2}}}) and ({{{-2}}},{{{4}}})  is:{{{y=(-2/5)x+16/5}}}

The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-2/5}}} and the y-intercept is {{{b=16/5}}}

Notice if we graph the equation {{{y=(-2/5)x+16/5}}} and plot the points ({{{3}}},{{{2}}}) and ({{{-2}}},{{{4}}}),  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, -6, 12,
graph(500, 500, -8.5, 9.5, -6, 12,(-2/5)x+16/5),
circle(3,2,0.12),
circle(3,2,0.12+0.03),
circle(-2,4,0.12),
circle(-2,4,0.12+0.03)
) }}} Graph of {{{y=(-2/5)x+16/5}}} through the points ({{{3}}},{{{2}}}) and ({{{-2}}},{{{4}}})

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