Question 221024
First let's find the slope of the line through the points *[Tex \LARGE \left(7,10\right)] and *[Tex \LARGE \left(-1,-1\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,10\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=10}}}.

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



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



{{{m=(-1-10)/(-1-7)}}} Plug in {{{y[2]=-1}}}, {{{y[1]=10}}}, {{{x[2]=-1}}}, and {{{x[1]=7}}}



{{{m=(-11)/(-1-7)}}} Subtract {{{10}}} from {{{-1}}} to get {{{-11}}}



{{{m=(-11)/(-8)}}} Subtract {{{7}}} from {{{-1}}} to get {{{-8}}}



{{{m=11/8}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,10\right)] and *[Tex \LARGE \left(-1,-1\right)] is {{{m=11/8}}}



Now let's use the point slope formula:



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



{{{y-10=(11/8)(x-7)}}} Plug in {{{m=11/8}}}, {{{x[1]=7}}}, and {{{y[1]=10}}}



{{{y-10=(11/8)x+(11/8)(-7)}}} Distribute



{{{y-10=(11/8)x-77/8}}} Multiply



{{{y=(11/8)x-77/8+10}}} Add 10 to both sides. 



{{{y=(11/8)x+3/8}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(7,10\right)] and *[Tex \LARGE \left(-1,-1\right)] is {{{y=(11/8)x+3/8}}}