Question 316296
Only post one problem at a time please.


# 1




First let's find the slope of the line through the points *[Tex \LARGE \left(-2,-4\right)] and *[Tex \LARGE \left(-7,-2\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,-4\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=-4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-7,-2\right)].  So this means that {{{x[2]=-7}}} and {{{y[2]=-2}}}.



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



{{{m=(-2--4)/(-7--2)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=-4}}}, {{{x[2]=-7}}}, and {{{x[1]=-2}}}



{{{m=(2)/(-7--2)}}} Subtract {{{-4}}} from {{{-2}}} to get {{{2}}}



{{{m=(2)/(-5)}}} Subtract {{{-2}}} from {{{-7}}} to get {{{-5}}}



{{{m=-2/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-2,-4\right)] and *[Tex \LARGE \left(-7,-2\right)] is {{{m=-2/5}}}



Now let's use the point slope formula:



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



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



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



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



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



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



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



{{{y=(-2/5)x-24/5}}} Combine like terms.



So the equation that goes through the points *[Tex \LARGE \left(-2,-4\right)] and *[Tex \LARGE \left(-7,-2\right)] is {{{y=(-2/5)x-24/5}}}



I'll let you convert that to standard form.