Question 307209
# 1



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,-6\right)]. So this means that {{{x[1]=4}}} and {{{y[1]=-6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,7\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=7}}}.



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



{{{m=(7--6)/(-3-4)}}} Plug in {{{y[2]=7}}}, {{{y[1]=-6}}}, {{{x[2]=-3}}}, and {{{x[1]=4}}}



{{{m=(13)/(-3-4)}}} Subtract {{{-6}}} from {{{7}}} to get {{{13}}}



{{{m=(13)/(-7)}}} Subtract {{{4}}} from {{{-3}}} to get {{{-7}}}



{{{m=-13/7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,-6\right)] and *[Tex \LARGE \left(-3,7\right)] is {{{m=-13/7}}}



For #2, you need another point to find the equation of the line to get the x and y intercepts.