Question 118749
If the y-intercept is -8, then the line goes through the point (0,-8)



First lets find the slope through the points ({{{-3}}},{{{1}}}) and ({{{0}}},{{{-8}}})


{{{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 ({{{-3}}},{{{1}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{0}}},{{{-8}}}))


{{{m=(-8-1)/(0--3)}}} Plug in {{{y[2]=-8}}},{{{y[1]=1}}},{{{x[2]=0}}},{{{x[1]=-3}}}  (these are the coordinates of given points)


{{{m= -9/3}}} Subtract the terms in the numerator {{{-8-1}}} to get {{{-9}}}.  Subtract the terms in the denominator {{{0--3}}} to get {{{3}}}

  


{{{m=-3}}} Reduce

  

So the slope is

{{{m=-3}}}


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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-1=(-3)(x--3)}}} Plug in {{{m=-3}}}, {{{x[1]=-3}}}, and {{{y[1]=1}}} (these values are given)



{{{y-1=(-3)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{y-1=-3x+(-3)(3)}}} Distribute {{{-3}}}


{{{y-1=-3x-9}}} Multiply {{{-3}}} and {{{3}}} to get {{{-9}}}


{{{y=-3x-9+1}}} Add {{{1}}} to  both sides to isolate y


{{{y=-3x-8}}} Combine like terms {{{-9}}} and {{{1}}} to get {{{-8}}} 

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Answer:



So the equation of the line which goes through the points ({{{-3}}},{{{1}}}) and ({{{0}}},{{{-8}}})  is:{{{y=-3x-8}}}


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-3}}} and the y-intercept is {{{b=-8}}}


Notice if we graph the equation {{{y=-3x-8}}} and plot the points ({{{-3}}},{{{1}}}) and ({{{0}}},{{{-8}}}),  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, -10.5, 7.5, -12.5, 5.5,
graph(500, 500, -10.5, 7.5, -12.5, 5.5,(-3)x+-8),
circle(-3,1,0.12),
circle(-3,1,0.12+0.03),
circle(0,-8,0.12),
circle(0,-8,0.12+0.03)
) }}} Graph of {{{y=-3x-8}}} through the points ({{{-3}}},{{{1}}}) and ({{{0}}},{{{-8}}})


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