Question 172181

First let's find the slope of the line through the points *[Tex \LARGE \left(1,-14\right)] and *[Tex \LARGE \left(-2,7\right)]



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



{{{m=(7--14)/(-2-1)}}} Plug in {{{y[2]=7}}}, {{{y[1]=-14}}}, {{{x[2]=-2}}}, and {{{x[1]=1}}}



{{{m=(21)/(-2-1)}}} Subtract {{{-14}}} from {{{7}}} to get {{{21}}}



{{{m=(21)/(-3)}}} Subtract {{{1}}} from {{{-2}}} to get {{{-3}}}



{{{m=-7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(1,-14\right)] and *[Tex \LARGE \left(-2,7\right)] is {{{m=-7}}}



Now let's use the point slope formula:



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



{{{y--14=-7(x-1)}}} Plug in {{{m=-7}}}, {{{x[1]=1}}}, and {{{y[1]=-14}}}



{{{y+14=-7(x-1)}}} Rewrite {{{y--14}}} as {{{y+14}}}



{{{y+14=-7x+-7(-1)}}} Distribute



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



{{{y=-7x+7-14}}} Subtract 14 from both sides. 



{{{y=-7x-7}}} Combine like terms. 




So the equation that goes through the points *[Tex \LARGE \left(1,-14\right)] and *[Tex \LARGE \left(-2,7\right)] is {{{y=-7x-7}}}



 Notice how the graph of {{{y=-7x-7}}} goes through the points *[Tex \LARGE \left(1,-14\right)] and *[Tex \LARGE \left(-2,7\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -15, 8,
 graph( 500, 500, -10, 10, -15, 8,-7x-7),
 circle(1,-14,0.08),
 circle(1,-14,0.10),
 circle(1,-14,0.12),
 circle(-2,7,0.08),
 circle(-2,7,0.10),
 circle(-2,7,0.12)
 )}}} Graph of {{{y=-7x-7}}} through the points *[Tex \LARGE \left(1,-14\right)] and *[Tex \LARGE \left(-2,7\right)]