Question 322837

First let's find the slope of the line through the points *[Tex \LARGE \left(2,0\right)] and *[Tex \LARGE \left(-2,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,0\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=0}}}.

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



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



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



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



{{{m=(5)/(-4)}}} Subtract {{{2}}} from {{{-2}}} to get {{{-4}}}



{{{m=-5/4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,0\right)] and *[Tex \LARGE \left(-2,5\right)] is {{{m=-5/4}}}



Now let's use the point slope formula:



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



{{{y-0=(-5/4)(x-2)}}} Plug in {{{m=-5/4}}}, {{{x[1]=2}}}, and {{{y[1]=0}}}



{{{y=(-5/4)(x-2)}}} Simplify



{{{y=(-5/4)x+(-5/4)(-2)}}} Distribute



{{{y=(-5/4)x+5/2}}} Multiply and reduce.



So the equation that goes through the points *[Tex \LARGE \left(2,0\right)] and *[Tex \LARGE \left(-2,5\right)] is {{{y=(-5/4)x+5/2}}}