Question 150557
First, let's find the slope of the line through the points (3, -8) and (-3, 9). 




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



{{{m=(9--8)/(-3-3)}}} Plug in {{{y[2]=9}}}, {{{y[1]=-8}}}, {{{x[2]=-3}}}, {{{x[1]=3}}}, , 



{{{m=(17)/(-3-3)}}} Subtract {{{-8}}} from {{{9}}} to get {{{17}}}



{{{m=(17)/(-6)}}} Subtract {{{3}}} from {{{-3}}} to get {{{-6}}}



{{{m=-17/6}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(3,-8\right)] and *[Tex \LARGE \left(-3,9\right)] is {{{m=-17/6}}}



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Now let's find the slope of the line through the points (-1, -5) and (-7, 12). 





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



{{{m=(12--5)/(-7--1)}}} Plug in {{{y[2]=12}}}, {{{y[1]=-5}}}, {{{x[2]=-7}}}, {{{x[1]=-1}}}, , 



{{{m=(17)/(-7--1)}}} Subtract {{{-5}}} from {{{12}}} to get {{{17}}}



{{{m=(17)/(-6)}}} Subtract {{{-1}}} from {{{-7}}} to get {{{-6}}}



{{{m=-17/6}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,-5\right)] and *[Tex \LARGE \left(-7,12\right)] is {{{m=-17/6}}}




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Since the slopes of the lines through both pairs of points are both {{{m=-17/6}}}, this means that the two slopes are equal. So this means that the two lines are parallel.



To verify this, we can simply graph the points and lines and we'll see that the two lines are parallel


 {{{drawing( 500, 500, -10, 10, -8, 15,
 grid(1),
 graph( 500, 500, -10, 10, -8, 15,(-17/6)x+1/2,(-17/6)x-47/6),
 circle(3,-8,0.08),
 circle(3,-8,0.10),
 circle(3,-8,0.12),
 circle(-3,9,0.08),
 circle(-3,9,0.10),
 circle(-3,9,0.12),

 circle(-1,-5,0.08),
 circle(-1,-5,0.10),
 circle(-1,-5,0.12),
 circle(-7,12,0.08),
 circle(-7,12,0.10),
 circle(-7,12,0.12)
 )}}}