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=(-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-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)]