Question 321515

First let's find the slope of the line through the points *[Tex \LARGE \left(5,-4\right)] and *[Tex \LARGE \left(1,-2\right)]

Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,-4\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=-4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,-2\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=-2}}}.

{{{m=(-2--4)/(1-5)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=-4}}}, {{{x[2]=1}}}, and {{{x[1]=5}}}

{{{m=(2)/(1-5)}}} Subtract {{{-4}}} from {{{-2}}} to get {{{2}}}

{{{m=(2)/(-4)}}} Subtract {{{5}}} from {{{1}}} to get {{{-4}}}

{{{m=-1/2}}} Reduce

So the slope of the line that goes through the points *[Tex \LARGE \left(5,-4\right)] and *[Tex \LARGE \left(1,-2\right)] is {{{m=-1/2}}}

Now let's use the point slope formula:

{{{y--4=(-1/2)(x-5)}}} Plug in {{{m=-1/2}}}, {{{x[1]=5}}}, and {{{y[1]=-4}}}

{{{y+4=(-1/2)(x-5)}}} Rewrite {{{y--4}}} as {{{y+4}}}

{{{y+4=(-1/2)x+(-1/2)(-5)}}} Distribute

{{{y+4=(-1/2)x+5/2}}} Multiply

{{{y=(-1/2)x+5/2-4}}} Subtract 4 from both sides.

{{{y=(-1/2)x-3/2}}} Combine like terms.

So the equation that goes through the points *[Tex \LARGE \left(5,-4\right)] and *[Tex \LARGE \left(1,-2\right)] is {{{y=(-1/2)x-3/2}}}