Question 302337
First let's find the slope of the line through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(-3,20\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,5\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,20\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=20}}}.



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



{{{m=(20-5)/(-3-0)}}} Plug in {{{y[2]=20}}}, {{{y[1]=5}}}, {{{x[2]=-3}}}, and {{{x[1]=0}}}



{{{m=(15)/(-3-0)}}} Subtract {{{5}}} from {{{20}}} to get {{{15}}}



{{{m=(15)/(-3)}}} Subtract {{{0}}} from {{{-3}}} to get {{{-3}}}



{{{m=-5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(-3,20\right)] is {{{m=-5}}}



Now let's use the point slope formula:



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



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



{{{y-5=-5x+5(0)}}} Distribute



{{{y-5=-5x+0}}} Multiply



{{{y=-5x+0+5}}} Add 5 to both sides. 



{{{y=-5x+5}}} Combine like terms. 




So the equation that goes through the points *[Tex \LARGE \left(0,5\right)] and *[Tex \LARGE \left(-3,20\right)] is {{{y=-5x+5}}}