Question 600365


First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(-9,-2\right)]



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



{{{m=(-2--3)/(-9--5)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=-3}}}, {{{x[2]=-9}}}, and {{{x[1]=-5}}}



{{{m=(1)/(-9--5)}}} Subtract {{{-3}}} from {{{-2}}} to get {{{1}}}



{{{m=(1)/(-4)}}} Subtract {{{-5}}} from {{{-9}}} to get {{{-4}}}



{{{m=-1/4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(-9,-2\right)] is {{{m=-1/4}}}



Now let's use the point slope formula:



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



{{{y--3=(-1/4)(x--5)}}} Plug in {{{m=-1/4}}}, {{{x[1]=-5}}}, and {{{y[1]=-3}}}



{{{y--3=(-1/4)(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+3=(-1/4)(x+5)}}} Rewrite {{{y--3}}} as {{{y+3}}}



{{{y+3=(-1/4)x+(-1/4)(5)}}} Distribute



{{{y+3=(-1/4)x-5/4}}} Multiply



{{{y=(-1/4)x-5/4-3}}} Subtract 3 from both sides. 



{{{y=(-1/4)x-17/4}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



So the equation that goes through the points *[Tex \LARGE \left(-5,-3\right)] and *[Tex \LARGE \left(-9,-2\right)] is {{{y=(-1/4)x-17/4}}}