Question 487054
First let's find the slope of the line through the points *[Tex \LARGE \left(-2,7\right)] and *[Tex \LARGE \left(-7,12\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,7\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=7}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-7,12\right)].  So this means that {{{x[2]=-7}}} and {{{y[2]=12}}}.



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



{{{m=(12-7)/(-7--2)}}} Plug in {{{y[2]=12}}}, {{{y[1]=7}}}, {{{x[2]=-7}}}, and {{{x[1]=-2}}}



{{{m=(5)/(-7--2)}}} Subtract {{{7}}} from {{{12}}} to get {{{5}}}



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



{{{m=-1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-2,7\right)] and *[Tex \LARGE \left(-7,12\right)] is {{{m=-1}}}



Now let's use the point slope formula:



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



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



{{{y-7=-1(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y-7=-1x+-1(2)}}} Distribute



{{{y-7=-1x-2}}} Multiply



{{{y=-1x-2+7}}} Add 7 to both sides. 



{{{y=-1x+5}}} Combine like terms. 



{{{y=-x+5}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-2,7\right)] and *[Tex \LARGE \left(-7,12\right)] is {{{y=-x+5}}}