Question 506997


First let's find the slope of the line through the points *[Tex \LARGE \left(2,7\right)] and *[Tex \LARGE \left(-2,9\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(-2,9\right)].  So this means that {{{x[2]=-2}}} and {{{y[2]=9}}}.



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



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



{{{m=(2)/(-2-2)}}} Subtract {{{7}}} from {{{9}}} to get {{{2}}}



{{{m=(2)/(-4)}}} Subtract {{{2}}} from {{{-2}}} to get {{{-4}}}



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



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



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



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



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



{{{y=(-1/2)x+8}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(2,7\right)] and *[Tex \LARGE \left(-2,9\right)] is {{{y=(-1/2)x+8}}}



 Notice how the graph of {{{y=(-1/2)x+8}}} goes through the points *[Tex \LARGE \left(2,7\right)] and *[Tex \LARGE \left(-2,9\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(-1/2)x+8),
 circle(2,7,0.08),
 circle(2,7,0.10),
 circle(2,7,0.12),
 circle(-2,9,0.08),
 circle(-2,9,0.10),
 circle(-2,9,0.12)
 )}}} Graph of {{{y=(-1/2)x+8}}} through the points *[Tex \LARGE \left(2,7\right)] and *[Tex \LARGE \left(-2,9\right)]



Let me know if you need more help or if you need me to explain a step in more detail.
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Thanks,


Jim