Question 555791


First let's find the slope of the line through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(2,13\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,5\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(2,13\right)].  So this means that {{{x[2]=2}}} and {{{y[2]=13}}}.



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



{{{m=(13-5)/(2-0)}}} Plug in {{{y[2]=13}}}, {{{y[1]=5}}}, {{{x[2]=2}}}, and {{{x[1]=0}}}



{{{m=(8)/(2-0)}}} Subtract {{{5}}} from {{{13}}} to get {{{8}}}



{{{m=(8)/(2)}}} Subtract {{{0}}} from {{{2}}} to get {{{2}}}



{{{m=4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(2,13\right)] is {{{m=4}}}



Now let's use the point slope formula:



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



{{{y-5=4(x-0)}}} Plug in {{{m=4}}}, {{{x[1]=0}}}, and {{{y[1]=5}}}



{{{y-5=4x+4(-0)}}} Distribute



{{{y-5=4x+0}}} Multiply



{{{y=4x+0+5}}} Add 5 to both sides. 



{{{y=4x+5}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(2,13\right)] is {{{y=4x+5}}}


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