Question 177464


First let's find the slope of the line through the points *[Tex \LARGE \left(2,-5\right)] and *[Tex \LARGE \left(-1,4\right)]



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



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



{{{m=(9)/(-1-2)}}} Subtract {{{-5}}} from {{{4}}} to get {{{9}}}



{{{m=(9)/(-3)}}} Subtract {{{2}}} from {{{-1}}} to get {{{-3}}}



{{{m=-3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,-5\right)] and *[Tex \LARGE \left(-1,4\right)] is {{{m=-3}}}



Now let's use the point slope formula:



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



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



{{{y+5=-3(x-2)}}} Rewrite {{{y--5}}} as {{{y+5}}}



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



{{{y+5=-3x+6}}} Multiply



{{{y=-3x+6-5}}} Subtract 5 from both sides. 



{{{y=-3x+1}}} Combine like terms. 



{{{y=-3x+1}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(2,-5\right)] and *[Tex \LARGE \left(-1,4\right)] is {{{y=-3x+1}}}



 Notice how the graph of {{{y=-3x+1}}} goes through the points *[Tex \LARGE \left(2,-5\right)] and *[Tex \LARGE \left(-1,4\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,-3x+1),
 circle(2,-5,0.08),
 circle(2,-5,0.10),
 circle(2,-5,0.12),
 circle(-1,4,0.08),
 circle(-1,4,0.10),
 circle(-1,4,0.12)
 )}}} Graph of {{{y=-3x+1}}} through the points *[Tex \LARGE \left(2,-5\right)] and *[Tex \LARGE \left(-1,4\right)]