Question 714887


First let's find the slope of the line through the points *[Tex \LARGE \left(2,10\right)] and *[Tex \LARGE \left(1,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,10\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=10}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,5\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=5}}}.



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



{{{m=(5-10)/(1-2)}}} Plug in {{{y[2]=5}}}, {{{y[1]=10}}}, {{{x[2]=1}}}, and {{{x[1]=2}}}



{{{m=(-5)/(1-2)}}} Subtract {{{10}}} from {{{5}}} to get {{{-5}}}



{{{m=(-5)/(-1)}}} Subtract {{{2}}} from {{{1}}} to get {{{-1}}}



{{{m=5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,10\right)] and *[Tex \LARGE \left(1,5\right)] is {{{m=5}}}



Now let's use the point slope formula:



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



{{{y-10=5(x-2)}}} Plug in {{{m=5}}}, {{{x[1]=2}}}, and {{{y[1]=10}}}



{{{y-10=5x+5(-2)}}} Distribute



{{{y-10=5x-10}}} Multiply



{{{y=5x-10+10}}} Add 10 to both sides. 



{{{y=5x+0}}} Combine like terms. 



{{{y=5x}}} Remove the trailing zero



So the equation that goes through the points *[Tex \LARGE \left(2,10\right)] and *[Tex \LARGE \left(1,5\right)] is {{{y=5x}}}