Question 357153
First let's find the slope of the line through the points *[Tex \LARGE \left(-3,2\right)] and *[Tex \LARGE \left(4,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-3,2\right)]. So this means that {{{x[1]=-3}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,5\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=5}}}.



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



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



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



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



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



Now let's use the point slope formula:



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



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



{{{y-2=(3/7)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{y-2=(3/7)x+(3/7)(3)}}} Distribute



{{{y-2=(3/7)x+9/7}}} Multiply



{{{y=(3/7)x+9/7+2}}} Add 2 to both sides. 



{{{y=(3/7)x+23/7}}} 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(-3,2\right)] and *[Tex \LARGE \left(4,5\right)] is {{{y=(3/7)x+23/7}}}



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Jim