Question 555818


First let's find the slope of the line through the points *[Tex \LARGE \left(-1,6\right)] and *[Tex \LARGE \left(1,7\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-1,6\right)]. So this means that {{{x[1]=-1}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,7\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=7}}}.



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



{{{m=(7-6)/(1--1)}}} Plug in {{{y[2]=7}}}, {{{y[1]=6}}}, {{{x[2]=1}}}, and {{{x[1]=-1}}}



{{{m=(1)/(1--1)}}} Subtract {{{6}}} from {{{7}}} to get {{{1}}}



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



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,6\right)] and *[Tex \LARGE \left(1,7\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-6=(1/2)(x--1)}}} Plug in {{{m=1/2}}}, {{{x[1]=-1}}}, and {{{y[1]=6}}}



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



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



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



{{{y=(1/2)x+1/2+6}}} Add 6 to both sides. 



{{{y=(1/2)x+13/2}}} 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(-1,6\right)] and *[Tex \LARGE \left(1,7\right)] is {{{y=(1/2)x+13/2}}}

 

The equation is y = mx+b form where m is the slope and (0, b) is the y intercept 



So because m = 1/2, we see that the slope is 1/2



Since b = 13/2, the y-intercept is (0, 13/2)


<b><font size=4>If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com">jim_thompson5910@hotmail.com</a>


Also, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Thank you


Jim</font></b>