Question 176421

First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(7,-3\right)]



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



{{{m=(-3--3)/(7--5)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=-3}}}, {{{x[2]=7}}}, and {{{x[1]=-5}}}



{{{m=(0)/(7--5)}}} Subtract {{{-3}}} from {{{-3}}} to get {{{0}}}



{{{m=(0)/(12)}}} Subtract {{{-5}}} from {{{7}}} to get {{{12}}}



{{{m=0}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(7,-3\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--3=0(x--5)}}} Plug in {{{m=0}}}, {{{x[1]=-5}}}, and {{{y[1]=-3}}}



{{{y--3=0(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+3=0(x+5)}}} Rewrite {{{y--3}}} as {{{y+3}}}



{{{y+3=0x+0(5)}}} Distribute



{{{y+3=0x+0}}} Multiply



{{{y=0x+0-3}}} Subtract 3 from both sides. 



{{{y=0x-3}}} Combine like terms. 



{{{y=-3}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(7,-3\right)] is {{{y=-3}}}



 Notice how the graph of {{{y=-3}}} goes through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(7,-3\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,-3),
 circle(-5,-3,0.08),
 circle(-5,-3,0.10),
 circle(-5,-3,0.12),
 circle(7,-3,0.08),
 circle(7,-3,0.10),
 circle(7,-3,0.12)
 )}}} Graph of {{{y=-3}}} through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(7,-3\right)]