Question 102633
First lets find the slope through the points ({{{4}}},{{{-4}}}) and ({{{2}}},{{{0}}})


{{{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 ({{{4}}},{{{-4}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{2}}},{{{0}}}))


{{{m=(0--4)/(2-4)}}} Plug in {{{y[2]=0}}},{{{y[1]=-4}}},{{{x[2]=2}}},{{{x[1]=4}}}  (these are the coordinates of given points)


{{{m= 4/-2}}} Subtract the terms in the numerator {{{0--4}}} to get {{{4}}}.  Subtract the terms in the denominator {{{2-4}}} to get {{{-2}}}

  


{{{m=-2}}} Reduce

  

So the slope is

{{{m=-2}}}


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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--4=(-2)(x-4)}}} Plug in {{{m=-2}}}, {{{x[1]=4}}}, and {{{y[1]=-4}}} (these values are given)



{{{y+4=(-2)(x-4)}}} Rewrite {{{y--4}}} as {{{y+4}}}



{{{y+4=-2x+(-2)(-4)}}} Distribute {{{-2}}}


{{{y+4=-2x+8}}} Multiply {{{-2}}} and {{{-4}}} to get {{{8}}}


{{{y=-2x+8-4}}} Subtract {{{4}}} from  both sides to isolate y


{{{y=-2x+4}}} Combine like terms {{{8}}} and {{{-4}}} to get {{{4}}} 

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Answer:



So the equation of the line which goes through the points ({{{4}}},{{{-4}}}) and ({{{2}}},{{{0}}})  is:{{{y=-2x+4}}}


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


Notice if we graph the equation {{{y=-2x+4}}} and plot the points ({{{4}}},{{{-4}}}) and ({{{2}}},{{{0}}}),  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, -6, 12, -11, 7,
graph(500, 500, -6, 12, -11, 7,(-2)x+4),
circle(4,-4,0.12),
circle(4,-4,0.12+0.03),
circle(2,0,0.12),
circle(2,0,0.12+0.03)
) }}} Graph of {{{y=-2x+4}}} through the points ({{{4}}},{{{-4}}}) and ({{{2}}},{{{0}}})


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