Question 164448


First let's find the slope of the line through the points *[Tex \LARGE \left(1,16\right)] and *[Tex \LARGE \left(-2,-16\right)]



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



{{{m=(-16-16)/(-2-1)}}} Plug in {{{y[2]=-16}}}, {{{y[1]=16}}}, {{{x[2]=-2}}}, and {{{x[1]=1}}}



{{{m=(-32)/(-2-1)}}} Subtract {{{16}}} from {{{-16}}} to get {{{-32}}}



{{{m=(-32)/(-3)}}} Subtract {{{1}}} from {{{-2}}} to get {{{-3}}}



{{{m=32/3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(1,16\right)] and *[Tex \LARGE \left(-2,-16\right)] is {{{m=32/3}}}



Now let's use the point slope formula:



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



{{{y-16=(32/3)(x-1)}}} Plug in {{{m=32/3}}}, {{{x[1]=1}}}, and {{{y[1]=16}}}



{{{y-16=(32/3)x+(32/3)(-1)}}} Distribute



{{{y-16=(32/3)x-32/3}}} Multiply



{{{y=(32/3)x-32/3+16}}} Add 16 to both sides. 



{{{y=(32/3)x+16/3}}} 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>.



{{{y=(32/3)x+16/3}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(1,16\right)] and *[Tex \LARGE \left(-2,-16\right)] is {{{y=(32/3)x+16/3}}}