Question 550603


First let's find the slope of the line through the points *[Tex \LARGE \left(9,-2\right)] and *[Tex \LARGE \left(4,6\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(9,-2\right)]. So this means that {{{x[1]=9}}} and {{{y[1]=-2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,6\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=6}}}.



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



{{{m=(6--2)/(4-9)}}} Plug in {{{y[2]=6}}}, {{{y[1]=-2}}}, {{{x[2]=4}}}, and {{{x[1]=9}}}



{{{m=(8)/(4-9)}}} Subtract {{{-2}}} from {{{6}}} to get {{{8}}}



{{{m=(8)/(-5)}}} Subtract {{{9}}} from {{{4}}} to get {{{-5}}}



{{{m=-8/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(9,-2\right)] and *[Tex \LARGE \left(4,6\right)] is {{{m=-8/5}}}



Now let's use the point slope formula:



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



{{{y--2=(-8/5)(x-9)}}} Plug in {{{m=-8/5}}}, {{{x[1]=9}}}, and {{{y[1]=-2}}}



{{{y+2=(-8/5)(x-9)}}} Rewrite {{{y--2}}} as {{{y+2}}}



{{{y+2=(-8/5)x+(-8/5)(-9)}}} Distribute



{{{y+2=(-8/5)x+72/5}}} Multiply



{{{y=(-8/5)x+72/5-2}}} Subtract 2 from both sides. 



{{{y=(-8/5)x+62/5}}} 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(9,-2\right)] and *[Tex \LARGE \left(4,6\right)] is {{{y=(-8/5)x+62/5}}}