Question 388731
First let's find the slope of the line through the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(10,-6\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(8,0\right)]. So this means that {{{x[1]=8}}} and {{{y[1]=0}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(10,-6\right)].  So this means that {{{x[2]=10}}} and {{{y[2]=-6}}}.



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



{{{m=(-6-0)/(10-8)}}} 



{{{m=(-6)/(2)}}} 



{{{m=-3}}} 





So the slope of the line that goes through the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(10,-6\right)] is {{{m=-3}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} 



{{{y-0=-3(x-8)}}} 



{{{y-0=-3x+-3(-8)}}} 



{{{y=-3x+24}}} 





So the equation that goes through the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(10,-6\right)] is {{{y=-3x+24}}}



 Notice how the graph of {{{y=-3x+24}}} goes through the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(10,-6\right)]. So this visually verifies our answer.

{{{drawing( 500, 500, -20, 20, -20, 20,
 graph( 500, 500, -20, 20, -20, 20,-3x+24),
 circle(4,0,0.08),
 circle(4,0,0.10),
 circle(4,0,0.12),
 circle(6,-8,0.08),
 circle(6,-8,0.10),
 circle(6,-8,0.12)
 )}}} Graph of {{{y=-3x+24}}} through the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(10,-6\right)]