Question 585488


First let's find the slope of the line through the points *[Tex \LARGE \left(5,4\right)] and *[Tex \LARGE \left(-2,0\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,4\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-2,0\right)].  So this means that {{{x[2]=-2}}} and {{{y[2]=0}}}.



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



{{{m=(0-4)/(-2-5)}}} Plug in {{{y[2]=0}}}, {{{y[1]=4}}}, {{{x[2]=-2}}}, and {{{x[1]=5}}}



{{{m=(-4)/(-2-5)}}} Subtract {{{4}}} from {{{0}}} to get {{{-4}}}



{{{m=(-4)/(-7)}}} Subtract {{{5}}} from {{{-2}}} to get {{{-7}}}



{{{m=4/7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,4\right)] and *[Tex \LARGE \left(-2,0\right)] is {{{m=4/7}}}



Now let's use the point slope formula:



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



{{{y-4=(4/7)(x-5)}}} Plug in {{{m=4/7}}}, {{{x[1]=5}}}, and {{{y[1]=4}}}



{{{y-4=(4/7)x+(4/7)(-5)}}} Distribute



{{{y-4=(4/7)x-20/7}}} Multiply



{{{y=(4/7)x-20/7+4}}} Add 4 to both sides. 



{{{y=(4/7)x+8/7}}} 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(5,4\right)] and *[Tex \LARGE \left(-2,0\right)] is {{{y=(4/7)x+8/7}}}


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