Question 94114
First lets find the slope through the points ({{{0}}},{{{2}}}) 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 ({{{0}}},{{{2}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{2}}},{{{0}}}))


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


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

  


{{{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-2=(-1)(x-0)}}} Plug in {{{m=-1}}}, {{{x[1]=0}}}, and {{{y[1]=2}}} (these values are given)



{{{y-2=-x+(-1)(0)}}} Distribute {{{-1}}}


{{{y-2=-x+0}}} Multiply {{{-1}}} and {{{0}}} to get {{{0}}}


{{{y=-x+0+2}}} Add {{{2}}} to  both sides to isolate y


{{{y=-x+2}}} Combine like terms {{{0}}} and {{{2}}} to get {{{2}}} 

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Answer:



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


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=2}}}


Notice if we graph the equation {{{y=-x+2}}} and plot the points ({{{0}}},{{{2}}}) 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, -8, 10, -8, 10,
graph(500, 500, -8, 10, -8, 10,(-1)x+2),
circle(0,2,0.12),
circle(0,2,0.12+0.03),
circle(2,0,0.12),
circle(2,0,0.12+0.03)
) }}} Graph of {{{y=-x+2}}} through the points ({{{0}}},{{{2}}}) and ({{{2}}},{{{0}}})


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