Question 173255

First let's find the slope of the line through the points *[Tex \LARGE \left(-3,7\right)] and *[Tex \LARGE \left(4,2\right)]



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



{{{m=(2-7)/(4--3)}}} Plug in {{{y[2]=2}}}, {{{y[1]=7}}}, {{{x[2]=4}}}, and {{{x[1]=-3}}}



{{{m=(-5)/(4--3)}}} Subtract {{{7}}} from {{{2}}} to get {{{-5}}}



{{{m=(-5)/(7)}}} Subtract {{{-3}}} from {{{4}}} to get {{{7}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-3,7\right)] and *[Tex \LARGE \left(4,2\right)] is {{{m=-5/7}}}



Now let's use the point slope formula:



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



{{{y-7=(-5/7)(x--3)}}} Plug in {{{m=-5/7}}}, {{{x[1]=-3}}}, and {{{y[1]=7}}}



{{{y-7=(-5/7)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{y-7=(-5/7)x+(-5/7)(3)}}} Distribute



{{{y-7=(-5/7)x-15/7}}} Multiply



{{{y=(-5/7)x-15/7+7}}} Add 7 to both sides. 



{{{y=(-5/7)x+34/7}}} 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(-3,7\right)] and *[Tex \LARGE \left(4,2\right)] is {{{y=(-5/7)x+34/7}}}