Question 623252


First let's find the slope of the line through the points *[Tex \LARGE \left(-20,9\right)] and *[Tex \LARGE \left(-15,4\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-20,9\right)]. So this means that {{{x[1]=-20}}} and {{{y[1]=9}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-15,4\right)].  So this means that {{{x[2]=-15}}} and {{{y[2]=4}}}.



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



{{{m=(4-9)/(-15--20)}}} Plug in {{{y[2]=4}}}, {{{y[1]=9}}}, {{{x[2]=-15}}}, and {{{x[1]=-20}}}



{{{m=(-5)/(-15--20)}}} Subtract {{{9}}} from {{{4}}} to get {{{-5}}}



{{{m=(-5)/(5)}}} Subtract {{{-20}}} from {{{-15}}} to get {{{5}}}



{{{m=-1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-20,9\right)] and *[Tex \LARGE \left(-15,4\right)] is {{{m=-1}}}



Now let's use the point slope formula:



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



{{{y-9=-1(x--20)}}} Plug in {{{m=-1}}}, {{{x[1]=-20}}}, and {{{y[1]=9}}}



{{{y-9=-1(x+20)}}} Rewrite {{{x--20}}} as {{{x+20}}}



{{{y-9=-1x+-1(20)}}} Distribute



{{{y-9=-1x-20}}} Multiply



{{{y=-1x-20+9}}} Add 9 to both sides. 



{{{y=-1x-11}}} Combine like terms. 



{{{y=-x-11}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-20,9\right)] and *[Tex \LARGE \left(-15,4\right)] is {{{y=-x-11}}}