Question 183633

First let's find the slope of the line through the points *[Tex \LARGE \left(7,3\right)] and *[Tex \LARGE \left(2,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,3\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(2,5\right)].



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



{{{m=(5-3)/(2-7)}}} Plug in {{{y[2]=5}}}, {{{y[1]=3}}}, {{{x[2]=2}}}, and {{{x[1]=7}}}



{{{m=(2)/(2-7)}}} Subtract {{{3}}} from {{{5}}} to get {{{2}}}



{{{m=(2)/(-5)}}} Subtract {{{7}}} from {{{2}}} to get {{{-5}}}



{{{m=-2/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,3\right)] and *[Tex \LARGE \left(2,5\right)] is {{{m=-2/5}}}



Now let's use the point slope formula:



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



{{{y-3=(-2/5)(x-7)}}} Plug in {{{m=-2/5}}}, {{{x[1]=7}}}, and {{{y[1]=3}}}



{{{y-3=(-2/5)x+(-2/5)(-7)}}} Distribute



{{{y-3=(-2/5)x+14/5}}} Multiply



{{{y=(-2/5)x+14/5+3}}} Add 3 to both sides. 



{{{y=(-2/5)x+29/5}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(7,3\right)] and *[Tex \LARGE \left(2,5\right)] is {{{y=(-2/5)x+29/5}}}