Question 670799


First let's find the slope of the line through the points *[Tex \LARGE \left(-1,0\right)] and *[Tex \LARGE \left(1,2\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-1,0\right)]. So this means that {{{x[1]=-1}}} and {{{y[1]=0}}}.

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



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



{{{m=(2-0)/(1--1)}}} Plug in {{{y[2]=2}}}, {{{y[1]=0}}}, {{{x[2]=1}}}, and {{{x[1]=-1}}}



{{{m=(2)/(1--1)}}} Subtract {{{0}}} from {{{2}}} to get {{{2}}}



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



{{{m=1}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,0\right)] and *[Tex \LARGE \left(1,2\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-0=1(x--1)}}} Plug in {{{m=1}}}, {{{x[1]=-1}}}, and {{{y[1]=0}}}



{{{y-0=1(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-0=1x+1(1)}}} Distribute



{{{y-0=1x+1}}} Multiply



{{{y=1x+1+0}}} Add 0 to both sides. 



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



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



So the equation that goes through the points *[Tex \LARGE \left(-1,0\right)] and *[Tex \LARGE \left(1,2\right)] is {{{y=x+1}}}



 Notice how the graph of {{{y=x+1}}} goes through the points *[Tex \LARGE \left(-1,0\right)] and *[Tex \LARGE \left(1,2\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,x+1),
 circle(-1,0,0.08),
 circle(-1,0,0.10),
 circle(-1,0,0.12),
 circle(1,2,0.08),
 circle(1,2,0.10),
 circle(1,2,0.12)
 )}}} Graph of {{{y=x+1}}} through the points *[Tex \LARGE \left(-1,0\right)] and *[Tex \LARGE \left(1,2\right)]