Question 550318


First let's find the slope of the line through the points *[Tex \LARGE \left(3,4\right)] and *[Tex \LARGE \left(-2,-5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,4\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-2,-5\right)].  So this means that {{{x[2]=-2}}} and {{{y[2]=-5}}}.



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



{{{m=(-5-4)/(-2-3)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=4}}}, {{{x[2]=-2}}}, and {{{x[1]=3}}}



{{{m=(-9)/(-2-3)}}} Subtract {{{4}}} from {{{-5}}} to get {{{-9}}}



{{{m=(-9)/(-5)}}} Subtract {{{3}}} from {{{-2}}} to get {{{-5}}}



{{{m=9/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(3,4\right)] and *[Tex \LARGE \left(-2,-5\right)] is {{{m=9/5}}}



Now let's use the point slope formula:



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



{{{y-4=(9/5)(x-3)}}} Plug in {{{m=9/5}}}, {{{x[1]=3}}}, and {{{y[1]=4}}}



{{{y-4=(9/5)x+(9/5)(-3)}}} Distribute



{{{y-4=(9/5)x-27/5}}} Multiply



{{{y=(9/5)x-27/5+4}}} Add 4 to both sides. 



{{{y=(9/5)x-7/5}}} 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(3,4\right)] and *[Tex \LARGE \left(-2,-5\right)] is {{{y=(9/5)x-7/5}}}