Question 150633

First let's find the slope of the line through the points *[Tex \LARGE \left(-12,-15\right)] and *[Tex \LARGE \left(-16,-6\right)]



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



{{{m=(-6--15)/(-16--12)}}} Plug in {{{y[2]=-6}}}, {{{y[1]=-15}}}, {{{x[2]=-16}}}, {{{x[1]=-12}}}, , 



{{{m=(9)/(-16--12)}}} Subtract {{{-15}}} from {{{-6}}} to get {{{9}}}



{{{m=(9)/(-4)}}} Subtract {{{-12}}} from {{{-16}}} to get {{{-4}}}



{{{m=-9/4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-12,-15\right)] and *[Tex \LARGE \left(-16,-6\right)] is {{{m=-9/4}}}



Now let's use the point slope formula:



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



{{{y--15=(-9/4)(x--12)}}} Plug in {{{m=-9/4}}}, {{{x[1]=-12}}}, and {{{y[1]=-15}}}



{{{y--15=(-9/4)(x+12)}}} Rewrite {{{x--12}}} as {{{x+12}}}



{{{y+15=(-9/4)(x+12)}}} Rewrite {{{y--15}}} as {{{y+15}}}



{{{y+15=(-9/4)x+(-9/4)(12)}}} Distribute



{{{y+15=(-9/4)x-27}}} Multiply



{{{y=(-9/4)x-27-15}}} Subtract 15 from both sides. 



{{{y=(-9/4)x-42}}} Combine like terms. 



{{{y=(-9/4)x-42}}} Simplify



{{{4y=4((-9/cross(4))x-42)}}} Multiply both sides by 4 to clear the fraction.



{{{4y=-9x-168}}} Distribute and multiply.



{{{4y+9x=-168}}} Add {{{9x}}} to both sides.



{{{9x+4y=-168}}} Rearrange the terms



So the equation in standard form that goes through the points *[Tex \LARGE \left(-12,-15\right)] and *[Tex \LARGE \left(-16,-6\right)] is {{{9x+4y=-168}}}