Question 551121

First let's find the slope of the line through the points *[Tex \LARGE \left(2,11\right)] and *[Tex \LARGE \left(7,26\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,11\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=11}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,26\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=26}}}.



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



{{{m=(26-11)/(7-2)}}} Plug in {{{y[2]=26}}}, {{{y[1]=11}}}, {{{x[2]=7}}}, and {{{x[1]=2}}}



{{{m=(15)/(7-2)}}} Subtract {{{11}}} from {{{26}}} to get {{{15}}}



{{{m=(15)/(5)}}} Subtract {{{2}}} from {{{7}}} to get {{{5}}}



{{{m=3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,11\right)] and *[Tex \LARGE \left(7,26\right)] is {{{m=3}}}



Now let's use the point slope formula:



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



{{{y-11=3(x-2)}}} Plug in {{{m=3}}}, {{{x[1]=2}}}, and {{{y[1]=11}}}



{{{y-11=3x+3(-2)}}} Distribute



{{{y-11=3x-6}}} Multiply



{{{y=3x-6+11}}} Add 11 to both sides. 



{{{y=3x+5}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(2,11\right)] and *[Tex \LARGE \left(7,26\right)] is {{{y=3x+5}}}