Question 916712


First let's find the slope of the line through the points *[Tex \LARGE \left(-4,2\right)] and *[Tex \LARGE \left(2,4\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-4,2\right)]. So this means that {{{x[1]=-4}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(2,4\right)].  So this means that {{{x[2]=2}}} and {{{y[2]=4}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(4-2)/(2--4)}}} Plug in {{{y[2]=4}}}, {{{y[1]=2}}}, {{{x[2]=2}}}, and {{{x[1]=-4}}}



{{{m=(2)/(2--4)}}} Subtract {{{2}}} from {{{4}}} to get {{{2}}}



{{{m=(2)/(6)}}} Subtract {{{-4}}} from {{{2}}} to get {{{6}}}



{{{m=1/3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-4,2\right)] and *[Tex \LARGE \left(2,4\right)] is {{{m=1/3}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y-2=(1/3)(x--4)}}} Plug in {{{m=1/3}}}, {{{x[1]=-4}}}, and {{{y[1]=2}}}



{{{y-2=(1/3)(x+4)}}} Rewrite {{{x--4}}} as {{{x+4}}}



{{{y-2=(1/3)x+(1/3)(4)}}} Distribute



{{{y-2=(1/3)x+4/3}}} Multiply



{{{y=(1/3)x+4/3+2}}} Add 2 to both sides. 



{{{y=(1/3)x+10/3}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



So the equation that goes through the points *[Tex \LARGE \left(-4,2\right)] and *[Tex \LARGE \left(2,4\right)] is {{{y=(1/3)x+10/3}}}


Let me know if you need more help or if you need me to explain a step in more detail.
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Thanks,


Jim