Question 177158


First let's find the slope of the line through the points *[Tex \LARGE \left(-4,1\right)] and *[Tex \LARGE \left(7,-5\right)]



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



{{{m=(-5-1)/(7--4)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=1}}}, {{{x[2]=7}}}, and {{{x[1]=-4}}}



{{{m=(-6)/(7--4)}}} Subtract {{{1}}} from {{{-5}}} to get {{{-6}}}



{{{m=(-6)/(11)}}} Subtract {{{-4}}} from {{{7}}} to get {{{11}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-4,1\right)] and *[Tex \LARGE \left(7,-5\right)] is {{{m=-6/11}}}



Now let's use the point slope formula:



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



{{{y-1=(-6/11)(x--4)}}} Plug in {{{m=-6/11}}}, {{{x[1]=-4}}}, and {{{y[1]=1}}}



{{{y-1=(-6/11)(x+4)}}} Rewrite {{{x--4}}} as {{{x+4}}}



{{{y-1=(-6/11)x+(-6/11)(4)}}} Distribute



{{{y-1=(-6/11)x-24/11}}} Multiply



{{{y=(-6/11)x-24/11+1}}} Add 1 to both sides. 



{{{y=(-6/11)x-13/11}}} 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(-4,1\right)] and *[Tex \LARGE \left(7,-5\right)] is {{{y=(-6/11)x-13/11}}}