Question 158284
The points *[Tex \LARGE \left(\frac{5}{3},-2\right)] and *[Tex \LARGE \left(3,6\right)] will be denoted *[Tex \LARGE \left(x_{1},y_{1}\right)] and *[Tex \LARGE \left(x_{2},y_{2}\right)]. So this means that , {{{x[1]=5/3}}}, {{{y[1]=-2}}}, {{{x[2]=3}}}, and {{{y[2]=6}}}




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



{{{m=(6--2)/(3-5/3)}}} Plug in {{{y[2]=6}}}, {{{y[1]=-2}}}, {{{x[2]=3}}}, and {{{x[1]=5/3}}}



{{{m=(8)/(3-5/3)}}} Subtract {{{-2}}} from {{{6}}} to get {{{8}}}



{{{m=(8)/(4/3)}}} Subtract {{{5/3}}} from {{{3}}} to get {{{4/3}}} (ie {{{3-5/3=9/3-5/3=4/3}}})



{{{m=(8)*(3/4)}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{m=6}}} Multiply and reduce.



So the slope of the line that goes through the points *[Tex \LARGE \left(\frac{5}{3},-2\right)] and *[Tex \LARGE \left(3,6\right)] is {{{m=6}}}