Question 117206
First lets find the slope through the points ({{{-6}}},{{{-9}}}) and ({{{1}}},{{{-9}}})


{{{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 ({{{-6}}},{{{-9}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{1}}},{{{-9}}}))


{{{m=(-9--9)/(1--6)}}} Plug in {{{y[2]=-9}}},{{{y[1]=-9}}},{{{x[2]=1}}},{{{x[1]=-6}}}  (these are the coordinates of given points)


{{{m= 0/7}}} Subtract the terms in the numerator {{{-9--9}}} to get {{{0}}}.  Subtract the terms in the denominator {{{1--6}}} to get {{{7}}}

  


{{{m=0}}} Reduce

  

So the slope is

{{{m=0}}}


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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--9=(0)(x--6)}}} Plug in {{{m=0}}}, {{{x[1]=-6}}}, and {{{y[1]=-9}}} (these values are given)



{{{y+9=(0)(x--6)}}} Rewrite {{{y--9}}} as {{{y+9}}}



{{{y+9=(0)(x+6)}}} Rewrite {{{x--6}}} as {{{x+6}}}



{{{y+9=0x+(0)(6)}}} Distribute {{{0}}}


{{{y+9=0x+0}}} Multiply {{{0}}} and {{{6}}} to get {{{0/0}}}. Now reduce {{{0/0}}} to get {{{0}}}


{{{y=0x+0-9}}} Subtract {{{9}}} from  both sides to isolate y


{{{y=0x-9}}} Combine like terms {{{0}}} and {{{-9}}} to get {{{-9}}} 



{{{y=-9}}} Remove the zero term

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Answer:



So the equation of the line which goes through the points ({{{-6}}},{{{-9}}}) and ({{{1}}},{{{-9}}})  is:{{{y=-9}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=0}}} and the y-intercept is {{{b=-9}}}


Notice if we graph the equation {{{y=-9}}} and plot the points ({{{-6}}},{{{-9}}}) and ({{{1}}},{{{-9}}}),  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, -11.5, 6.5, -18, 0,
graph(500, 500, -11.5, 6.5, -18, 0,(0)x+-9),
circle(-6,-9,0.12),
circle(-6,-9,0.12+0.03),
circle(1,-9,0.12),
circle(1,-9,0.12+0.03)
) }}} Graph of {{{y=-9}}} through the points ({{{-6}}},{{{-9}}}) and ({{{1}}},{{{-9}}})


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