Question 150341

First let's find the slope of the line through the points *[Tex \LARGE \left(-1,2\right)] and *[Tex \LARGE \left(3,4\right)]



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



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



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



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



{{{m=1/2}}} Reduce



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



Now let's use the point slope formula:



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



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



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



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



{{{y-2=(1/2)x+1/2}}} Multiply



{{{y=(1/2)x+1/2+2}}} Add 2 to both sides. 



{{{y=(1/2)x+5/2}}} 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(-1,2\right)] and *[Tex \LARGE \left(3,4\right)] is {{{y=(1/2)x+5/2}}}



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

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