Question 130982
First lets find the slope through the points ({{{-2}}},{{{-7}}}) and ({{{-9}}},{{{-5}}})


{{{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 ({{{-2}}},{{{-7}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{-9}}},{{{-5}}}))


{{{m=(-5--7)/(-9--2)}}} Plug in {{{y[2]=-5}}},{{{y[1]=-7}}},{{{x[2]=-9}}},{{{x[1]=-2}}}  (these are the coordinates of given points)


{{{m= 2/-7}}} Subtract the terms in the numerator {{{-5--7}}} to get {{{2}}}.  Subtract the terms in the denominator {{{-9--2}}} to get {{{-7}}}

  


{{{m=-2/7}}} Reduce

  

So the slope is

{{{m=-2/7}}}


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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=(-2/7)(x--2)}}} Plug in {{{m=-2/7}}}, {{{x[1]=-2}}}, and {{{y[1]=-7}}} (these values are given)



{{{y+7=(-2/7)(x--2)}}} Rewrite {{{y--7}}} as {{{y+7}}}



{{{y+7=(-2/7)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y+7=(-2/7)x+(-2/7)(2)}}} Distribute {{{-2/7}}}


{{{y+7=(-2/7)x-4/7}}} Multiply {{{-2/7}}} and {{{2}}} to get {{{-4/7}}}


{{{y=(-2/7)x-4/7-7}}} Subtract {{{7}}} from  both sides to isolate y


{{{y=(-2/7)x-53/7}}} Combine like terms {{{-4/7}}} and {{{-7}}} to get {{{-53/7}}} (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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Answer:



So the equation of the line which goes through the points ({{{-2}}},{{{-7}}}) and ({{{-9}}},{{{-5}}})  is:{{{y=(-2/7)x-53/7}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-2/7}}} and the y-intercept is {{{b=-53/7}}}


Notice if we graph the equation {{{y=(-2/7)x-53/7}}} and plot the points ({{{-2}}},{{{-7}}}) and ({{{-9}}},{{{-5}}}),  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, -14.5, 3.5, -15, 3,
graph(500, 500, -14.5, 3.5, -15, 3,(-2/7)x+-53/7),
circle(-2,-7,0.12),
circle(-2,-7,0.12+0.03),
circle(-9,-5,0.12),
circle(-9,-5,0.12+0.03)
) }}} Graph of {{{y=(-2/7)x-53/7}}} through the points ({{{-2}}},{{{-7}}}) and ({{{-9}}},{{{-5}}})


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