Question 152519

First let's find the slope of the line through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(4,2\right)]



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



{{{m=(2-3)/(4--2)}}} Plug in {{{y[2]=2}}}, {{{y[1]=3}}}, {{{x[2]=4}}}, {{{x[1]=-2}}}, , 



{{{m=(-1)/(4--2)}}} Subtract {{{3}}} from {{{2}}} to get {{{-1}}}



{{{m=(-1)/(6)}}} Subtract {{{-2}}} from {{{4}}} to get {{{6}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(4,2\right)] is {{{m=-1/6}}}



Now let's use the point slope formula:



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



{{{y-3=(-1/6)(x--2)}}} Plug in {{{m=-1/6}}}, {{{x[1]=-2}}}, and {{{y[1]=3}}}



{{{y-3=(-1/6)(x+2)}}} Rewrite {{{x--2}}} as {{{x+2}}}



{{{y-3=(-1/6)x+(-1/6)(2)}}} Distribute



{{{y-3=(-1/6)x-1/3}}} Multiply



{{{y=(-1/6)x-1/3+3}}} Add 3 to both sides. 



{{{y=(-1/6)x+8/3}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.




So the equation that goes through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(4,2\right)] is {{{y=(-1/6)x+8/3}}}



 Notice how the graph of {{{y=(-1/6)x+8/3}}} goes through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(4,2\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(-1/6)x+8/3),
 circle(-2,3,0.08),
 circle(-2,3,0.10),
 circle(-2,3,0.12),
 circle(4,2,0.08),
 circle(4,2,0.10),
 circle(4,2,0.12)
 )}}} Graph of {{{y=(-1/6)x+8/3}}} through the points *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(4,2\right)]