Question 228238

First let's find the slope of the line through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(9,-1\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(9,-1\right)].  So this means that {{{x[2]=9}}} and {{{y[2]=-1}}}.



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



{{{m=(-1-7)/(9--7)}}} Plug in {{{y[2]=-1}}}, {{{y[1]=7}}}, {{{x[2]=9}}}, and {{{x[1]=-7}}}



{{{m=(-8)/(9--7)}}} Subtract {{{7}}} from {{{-1}}} to get {{{-8}}}



{{{m=(-8)/(16)}}} Subtract {{{-7}}} from {{{9}}} to get {{{16}}}



{{{m=-1/2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(9,-1\right)] is {{{m=-1/2}}}



Now let's use the point slope formula:



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



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



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



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



{{{y-7=(-1/2)x-7/2}}} Multiply



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



{{{y=(-1/2)x+7/2}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(9,-1\right)] is {{{y=(-1/2)x+7/2}}}



 Notice how the graph of {{{y=(-1/2)x+7/2}}} goes through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(9,-1\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(-1/2)x+7/2),
 circle(-7,7,0.08),
 circle(-7,7,0.10),
 circle(-7,7,0.12),
 circle(9,-1,0.08),
 circle(9,-1,0.10),
 circle(9,-1,0.12)
 )}}} Graph of {{{y=(-1/2)x+7/2}}} through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(9,-1\right)]