Question 632514


First let's find the slope of the line through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(5,2\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,2\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=2}}}.



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



{{{m=(2-2)/(5--1)}}} Plug in {{{y[2]=2}}}, {{{y[1]=2}}}, {{{x[2]=5}}}, and {{{x[1]=-1}}}



{{{m=(0)/(5--1)}}} Subtract {{{2}}} from {{{2}}} to get {{{0}}}



{{{m=(0)/(6)}}} Subtract {{{-1}}} from {{{5}}} to get {{{6}}}



{{{m=0}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(5,2\right)] is {{{m=0}}}



Now let's use the point slope formula:



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



{{{y-2=0(x--1)}}} Plug in {{{m=0}}}, {{{x[1]=-1}}}, and {{{y[1]=2}}}



{{{y-2=0(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-2=0x+0(1)}}} Distribute



{{{y-2=0x+0}}} Multiply



{{{y=0x+0+2}}} Add 2 to both sides. 



{{{y=0x+2}}} Combine like terms. 



{{{y=2}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(5,2\right)] is {{{y=+2}}}



 Notice how the graph of {{{y=2}}} goes through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(5,2\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,+2),
 circle(-1,2,0.08),
 circle(-1,2,0.10),
 circle(-1,2,0.12),
 circle(5,2,0.08),
 circle(5,2,0.10),
 circle(5,2,0.12)
 )}}} Graph of {{{y=+2}}} through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(5,2\right)]


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