Question 595174


First let's find the slope of the line through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-1,8\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,5\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,8\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=8}}}.



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



{{{m=(8-5)/(-1-2)}}} Plug in {{{y[2]=8}}}, {{{y[1]=5}}}, {{{x[2]=-1}}}, and {{{x[1]=2}}}



{{{m=(3)/(-1-2)}}} Subtract {{{5}}} from {{{8}}} to get {{{3}}}



{{{m=(3)/(-3)}}} Subtract {{{2}}} from {{{-1}}} to get {{{-3}}}



{{{m=-1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-1,8\right)] is {{{m=-1}}}



Now let's use the point slope formula:



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



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



{{{y-5=-1x+-1(-2)}}} Distribute



{{{y-5=-1x+2}}} Multiply



{{{y=-1x+2+5}}} Add 5 to both sides. 



{{{y=-1x+7}}} Combine like terms. 



{{{y=-x+7}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-1,8\right)] is {{{y=-x+7}}}



 Notice how the graph of {{{y=-x+7}}} goes through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-1,8\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,-x+7),
 circle(2,5,0.08),
 circle(2,5,0.10),
 circle(2,5,0.12),
 circle(-1,8,0.08),
 circle(-1,8,0.10),
 circle(-1,8,0.12)
 )}}} Graph of {{{y=-x+7}}} through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-1,8\right)]