Question 626101


First let's find the slope of the line through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(-6,9\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-6,9\right)].  So this means that {{{x[2]=-6}}} and {{{y[2]=9}}}.



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



{{{m=(9-7)/(-6--7)}}} Plug in {{{y[2]=9}}}, {{{y[1]=7}}}, {{{x[2]=-6}}}, and {{{x[1]=-7}}}



{{{m=(2)/(-6--7)}}} Subtract {{{7}}} from {{{9}}} to get {{{2}}}



{{{m=(2)/(1)}}} Subtract {{{-7}}} from {{{-6}}} to get {{{1}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(-6,9\right)] is {{{m=2}}}



Now let's use the point slope formula:



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



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



{{{y-7=2(x+7)}}} Rewrite {{{x--7}}} as {{{x+7}}}



{{{y-7=2x+2(7)}}} Distribute



{{{y-7=2x+14}}} Multiply



{{{y=2x+14+7}}} Add 7 to both sides. 



{{{y=2x+21}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-7,7\right)] and *[Tex \LARGE \left(-6,9\right)] is {{{y=2x+21}}}



<font color="red">--------------------------------------------------------------------------------------------------------------</font>
If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">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 color="red">--------------------------------------------------------------------------------------------------------------</font>