Question 112041
First lets find the slope through the points ({{{-3}}},{{{-5}}}) and ({{{3}}},{{{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 ({{{-3}}},{{{-5}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{3}}},{{{0}}}))

{{{m=(0--5)/(3--3)}}} Plug in {{{y[2]=0}}},{{{y[1]=-5}}},{{{x[2]=3}}},{{{x[1]=-3}}}  (these are the coordinates of given points)

{{{m= 5/6}}} Subtract the terms in the numerator {{{0--5}}} to get {{{5}}}.  Subtract the terms in the denominator {{{3--3}}} to get {{{6}}}

So the slope is

{{{m=5/6}}}

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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--5=(5/6)(x--3)}}} Plug in {{{m=5/6}}}, {{{x[1]=-3}}}, and {{{y[1]=-5}}} (these values are given)

{{{y+5=(5/6)(x--3)}}} Rewrite {{{y--5}}} as {{{y+5}}}

{{{y+5=(5/6)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}

{{{y+5=(5/6)x+(5/6)(3)}}} Distribute {{{5/6}}}

{{{y+5=(5/6)x+5/2}}} Multiply {{{5/6}}} and {{{3}}} to get {{{15/6}}}. Now reduce {{{15/6}}} to get {{{5/2}}}

{{{y=(5/6)x+5/2-5}}} Subtract {{{5}}} from  both sides to isolate y

{{{y=(5/6)x-5/2}}} Combine like terms {{{5/2}}} and {{{-5}}} to get {{{-5/2}}} (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 ({{{-3}}},{{{-5}}}) and ({{{3}}},{{{0}}})  is:{{{y=(5/6)x-5/2}}}

The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=5/6}}} and the y-intercept is {{{b=-5/2}}}

Notice if we graph the equation {{{y=(5/6)x-5/2}}} and plot the points ({{{-3}}},{{{-5}}}) and ({{{3}}},{{{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, -9, 9, -11.5, 6.5,
graph(500, 500, -9, 9, -11.5, 6.5,(5/6)x+-5/2),
circle(-3,-5,0.12),
circle(-3,-5,0.12+0.03),
circle(3,0,0.12),
circle(3,0,0.12+0.03)
) }}} Graph of {{{y=(5/6)x-5/2}}} through the points ({{{-3}}},{{{-5}}}) and ({{{3}}},{{{0}}})

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