Question 116141
First lets find the slope through the points ({{{-15}}},{{{-7}}}) and ({{{18}}},{{{-7}}})


{{{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 ({{{-15}}},{{{-7}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{18}}},{{{-7}}}))


{{{m=(-7--7)/(18--15)}}} Plug in {{{y[2]=-7}}},{{{y[1]=-7}}},{{{x[2]=18}}},{{{x[1]=-15}}}  (these are the coordinates of given points)


{{{m= 0/33}}} Subtract the terms in the numerator {{{-7--7}}} to get {{{0}}}.  Subtract the terms in the denominator {{{18--15}}} to get {{{33}}}

  


{{{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--7=(0)(x--15)}}} Plug in {{{m=0}}}, {{{x[1]=-15}}}, and {{{y[1]=-7}}} (these values are given)



{{{y+7=(0)(x--15)}}} Rewrite {{{y--7}}} as {{{y+7}}}



{{{y+7=(0)(x+15)}}} Rewrite {{{x--15}}} as {{{x+15}}}



{{{y+7=0x+(0)(15)}}} Distribute {{{0}}}


{{{y+7=0x+0}}} Multiply {{{0}}} and {{{15}}} to get {{{0/0}}}. Now reduce {{{0/0}}} to get {{{0}}}


{{{y=0x+0-7}}} Subtract {{{7}}} from  both sides to isolate y


{{{y=0x-7}}} Combine like terms {{{0}}} and {{{-7}}} to get {{{-7}}} 



{{{y=-7}}} Remove the zero term

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Answer:



So the equation of the line which goes through the points ({{{-15}}},{{{-7}}}) and ({{{18}}},{{{-7}}})  is: {{{y=-7}}}


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=-7}}}


Notice if we graph the equation {{{y=-7}}} and plot the points ({{{-15}}},{{{-7}}}) and ({{{18}}},{{{-7}}}),  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, -20, 20, -16, 2,
graph(500, 500, -20, 20, -16, 2,(0)x+-7),
circle(-15,-7,0.18),
circle(-15,-7,0.18+0.03),
circle(18,-7,0.18),
circle(18,-7,0.18+0.03)
) }}} Graph of {{{y=-7}}} through the points ({{{-15}}},{{{-7}}}) and ({{{18}}},{{{-7}}})


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