Question 620573


First let's find the slope of the line through the points *[Tex \LARGE \left(3,6\right)] and *[Tex \LARGE \left(7,-2\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,6\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,-2\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=-2}}}.



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



{{{m=(-2-6)/(7-3)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=6}}}, {{{x[2]=7}}}, and {{{x[1]=3}}}



{{{m=(-8)/(7-3)}}} Subtract {{{6}}} from {{{-2}}} to get {{{-8}}}



{{{m=(-8)/(4)}}} Subtract {{{3}}} from {{{7}}} to get {{{4}}}



{{{m=-2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(3,6\right)] and *[Tex \LARGE \left(7,-2\right)] is {{{m=-2}}}



Now let's use the point slope formula:



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



{{{y-6=-2(x-3)}}} Plug in {{{m=-2}}}, {{{x[1]=3}}}, and {{{y[1]=6}}}



{{{y-6=-2x+-2(-3)}}} Distribute



{{{y-6=-2x+6}}} Multiply



{{{y=-2x+6+6}}} Add 6 to both sides. 



{{{y=-2x+12}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(3,6\right)] and *[Tex \LARGE \left(7,-2\right)] is {{{y=-2x+12}}}