Question 639641


First let's find the slope of the line through the points *[Tex \LARGE \left(2,1\right)] and *[Tex \LARGE \left(6,4\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,4\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=4}}}.



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



{{{m=(4-1)/(6-2)}}} Plug in {{{y[2]=4}}}, {{{y[1]=1}}}, {{{x[2]=6}}}, and {{{x[1]=2}}}



{{{m=(3)/(6-2)}}} Subtract {{{1}}} from {{{4}}} to get {{{3}}}



{{{m=(3)/(4)}}} Subtract {{{2}}} from {{{6}}} to get {{{4}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(2,1\right)] and *[Tex \LARGE \left(6,4\right)] is {{{m=3/4}}}



Now let's use the point slope formula:



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



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



{{{y-1=(3/4)x+(3/4)(-2)}}} Distribute



{{{y-1=(3/4)x-3/2}}} Multiply



{{{y=(3/4)x-3/2+1}}} Add 1 to both sides. 



{{{y=(3/4)x-1/2}}} 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(2,1\right)] and *[Tex \LARGE \left(6,4\right)] is {{{y=(3/4)x-1/2}}}