Question 286207
First let's find the slope of the line through the points *[Tex \LARGE \left(6,-14\right)] and *[Tex \LARGE \left(3,-2\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(6,-14\right)]. So this means that {{{x[1]=6}}} and {{{y[1]=-14}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,-2\right)].  So this means that {{{x[2]=3}}} and {{{y[2]=-2}}}.



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



{{{m=(-2--14)/(3-6)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=-14}}}, {{{x[2]=3}}}, and {{{x[1]=6}}}



{{{m=(12)/(3-6)}}} Subtract {{{-14}}} from {{{-2}}} to get {{{12}}}



{{{m=(12)/(-3)}}} Subtract {{{6}}} from {{{3}}} to get {{{-3}}}



{{{m=-4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(6,-14\right)] and *[Tex \LARGE \left(3,-2\right)] is {{{m=-4}}}



Now let's use the point slope formula:



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



{{{y--14=-4(x-6)}}} Plug in {{{m=-4}}}, {{{x[1]=6}}}, and {{{y[1]=-14}}}



{{{y+14=-4(x-6)}}} Rewrite {{{y--14}}} as {{{y+14}}}



{{{y+14=-4x+-4(-6)}}} Distribute



{{{y+14=-4x+24}}} Multiply



{{{y=-4x+24-14}}} Subtract 14 from both sides. 



{{{y=-4x+10}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(6,-14\right)] and *[Tex \LARGE \left(3,-2\right)] is {{{y=-4x+10}}}