Question 174350


First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-5\right)] and *[Tex \LARGE \left(4,-3\right)]



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



{{{m=(-3--5)/(4--5)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=-5}}}, {{{x[2]=4}}}, and {{{x[1]=-5}}}



{{{m=(2)/(4--5)}}} Subtract {{{-5}}} from {{{-3}}} to get {{{2}}}



{{{m=(2)/(9)}}} Subtract {{{-5}}} from {{{4}}} to get {{{9}}}



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



Now let's use the point slope formula:



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



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



{{{y--5=(2/9)(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+5=(2/9)(x+5)}}} Rewrite {{{y--5}}} as {{{y+5}}}



{{{y+5=(2/9)x+(2/9)(5)}}} Distribute



{{{y+5=(2/9)x+10/9}}} Multiply



{{{y=(2/9)x+10/9-5}}} Subtract 5 from both sides. 



{{{y=(2/9)x-35/9}}} 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>.



{{{y=(2/9)x-35/9}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(-5,-5\right)] and *[Tex \LARGE \left(4,-3\right)] is {{{y=(2/9)x-35/9}}}