Question 244833
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(\frac{3}{2},-3\right)]. So this means that {{{x[1]=3/2}}} and {{{y[1]=-3}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(0,\frac{2}{5}\right)].  So this means that {{{x[2]=0}}} and {{{y[2]=2/5}}}.



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



{{{m=(2/5--3)/(0-3/2)}}} Plug in {{{y[2]=2/5}}}, {{{y[1]=-3}}}, {{{x[2]=0}}}, and {{{x[1]=3/2}}}



{{{m=(17/5)/(0-3/2)}}} Subtract {{{-3}}} from {{{2/5}}} to get {{{2/5--3=2/5+3=2/5+15/5=(2+15)/5=17/5}}}



{{{m=(17/5)/(-3/2)}}} Subtract {{{3/2}}} from {{{0}}} to get {{{-3/2}}}



{{{m=(17/5)*(-2/3)}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{m=-34/15}}} Multiply.



So the slope of the line that goes through the points *[Tex \LARGE \left(\frac{3}{2},-3\right)] and *[Tex \LARGE \left(0,\frac{2}{5}\right)] is {{{m=-34/15}}}