Question 102458
First lets find the slope through the points ({{{-7/5}}},{{{3/10}}}) and ({{{1/5}}},{{{-1/2}}})

{{{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 ({{{-7/5}}},{{{3/10}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{1/5}}},{{{-1/2}}}))

{{{m=(-1/2-3/10)/(1/5--7/5)}}} Plug in {{{y[2]=-1/2}}},{{{y[1]=3/10}}},{{{x[2]=1/5}}},{{{x[1]=-7/5}}}  (these are the coordinates of given points)

{{{m= (-8 / 10)/(8 / 5)}}} Subtract   (note: if you need help with subtracting or dividing fractions, check out this <a href=http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver>solver</a>)

{{{m=-1 / 2}}} Divide the fractions

So the slope is

{{{m=-1 / 2}}}

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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-3/10=(-1 / 2)(x--7/5)}}} Plug in {{{m=-1 / 2}}}, {{{x[1]=-7/5}}}, and {{{y[1]=3/10}}} (these values are given)

{{{y-3/10=(-1 / 2)(x+7/5)}}} Rewrite {{{x--7/5}}} as {{{x+7/5}}}

{{{y-3/10=(-1/2)x+(-1/2)(7/5)}}} Distribute {{{-1 / 2}}}

{{{y-3/10=(-1/2)x-7/10}}} Multiply {{{-1 / 2}}} and {{{7/5}}} to get {{{-7/10}}}

{{{y=(-1/2)x-7/10+3/10}}} Add {{{3/10}}} to  both sides to isolate y

{{{y=(-1/2)x-2/5}}} Combine like terms {{{-7/10}}} and {{{3/10}}} to get {{{-2/5}}} (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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So the equation of the line which goes through the points ({{{-7/5}}},{{{3/10}}}) and ({{{1/5}}},{{{-1/2}}})  is:{{{y=(-1/2)x-2/5}}}

The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=-1 / 2}}} and the y-intercept is {{{b=-2/5}}}

Notice if we graph the equation {{{y=(-1/2)x-2/5}}} and plot the points ({{{-7/5}}},{{{3/10}}}) and ({{{1/5}}},{{{-1/2}}}),  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, -12, 6, -8, 10,
graph(500, 500, -12, 6, -8, 10,(-1 / 2)x+-2/5),
circle(-7/5,3/10,0.12),
circle(-7/5,3/10,0.12+0.03),
circle(1/5,-1/2,0.12),
circle(1/5,-1/2,0.12+0.03)
) }}} Graph of {{{y=(-1/2)x-2/5}}} through the points ({{{-7/5}}},{{{3/10}}}) and ({{{1/5}}},{{{-1/2}}})

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