Question 684045
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,-5\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=-5}}}.

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



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



{{{m=(4--5)/(4-7)}}} Plug in {{{y[2]=4}}}, {{{y[1]=-5}}}, {{{x[2]=4}}}, and {{{x[1]=7}}}



{{{m=(9)/(4-7)}}} Subtract {{{-5}}} from {{{4}}} to get {{{9}}}



{{{m=(9)/(-3)}}} Subtract {{{7}}} from {{{4}}} to get {{{-3}}}



{{{m=-3}}} Reduce



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



The angle of inclination is 


theta = arctan(rise/run)


theta = arctan(3/1) ... note: make the rise positive


theta = 71.56505


So the angle of inclination is roughly  71.56505 degrees