Question 458667

First let's find the slope of the line through the points *[Tex \LARGE \left(7,17\right)] and *[Tex \LARGE \left(15,33\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,17\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=17}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(15,33\right)].  So this means that {{{x[2]=15}}} and {{{y[2]=33}}}.



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



{{{m=(33-17)/(15-7)}}} Plug in {{{y[2]=33}}}, {{{y[1]=17}}}, {{{x[2]=15}}}, and {{{x[1]=7}}}



{{{m=(16)/(15-7)}}} Subtract {{{17}}} from {{{33}}} to get {{{16}}}



{{{m=(16)/(8)}}} Subtract {{{7}}} from {{{15}}} to get {{{8}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,17\right)] and *[Tex \LARGE \left(15,33\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-17=2(x-7)}}} Plug in {{{m=2}}}, {{{x[1]=7}}}, and {{{y[1]=17}}}



{{{y-17=2x+2(-7)}}} Distribute



{{{y-17=2x-14}}} Multiply



{{{y=2x-14+17}}} Add 17 to both sides. 



{{{y=2x+3}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(7,17\right)] and *[Tex \LARGE \left(15,33\right)] is {{{y=2x+3}}}