Question 867583


First let's find the slope of the line through the points *[Tex \LARGE \left(-1,4\right)] and *[Tex \LARGE \left(2,0\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-1,4\right)]. So this means that {{{x[1]=-1}}} 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--1)}}} Plug in {{{y[2]=0}}}, {{{y[1]=4}}}, {{{x[2]=2}}}, and {{{x[1]=-1}}}



{{{m=(-4)/(2--1)}}} Subtract {{{4}}} from {{{0}}} to get {{{-4}}}



{{{m=(-4)/(3)}}} Subtract {{{-1}}} from {{{2}}} to get {{{3}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,4\right)] and *[Tex \LARGE \left(2,0\right)] is {{{m=-4/3}}}



Now let's use the point slope formula:



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



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



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



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



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



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



{{{y=(-4/3)x+8/3}}} 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(-1,4\right)] and *[Tex \LARGE \left(2,0\right)] is {{{y=(-4/3)x+8/3}}}