Question 342045
{{{-3x-y=6}}} Start with the given equation.



{{{-y=6--3x}}} Add {{{3x}}} to both sides.



{{{-y=--3x+6}}} Rearrange the terms.



{{{y=(--3x+6)/(-1)}}} Divide both sides by {{{-1}}} to isolate y.



{{{y=((--3)/(-1))x+(6)/(-1)}}} Break up the fraction.



{{{y=-3x-6}}} Reduce.



Looking at {{{y=-3x-6}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=-3}}} and the y-intercept is {{{b=-6}}} 



Since {{{b=-6}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-6\right)].Remember the y-intercept is the point where the graph intersects with the y-axis


So we have one point *[Tex \LARGE \left(0,-6\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-6,.1)),
  blue(circle(0,-6,.12)),
  blue(circle(0,-6,.15))
)}}}



Now since the slope is comprised of the "rise" over the "run" this means

{{{slope=rise/run}}}


Also, because the slope is {{{-3}}}, this means:


{{{rise/run=-3/1}}}



which shows us that the rise is -3 and the run is 1. This means that to go from point to point, we can go down 3  and over 1




So starting at *[Tex \LARGE \left(0,-6\right)], go down 3 units 

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-6,.1)),
  blue(circle(0,-6,.12)),
  blue(circle(0,-6,.15)),
  blue(arc(0,-6+(-3/2),2,-3,90,270))
)}}}


and to the right 1 unit to get to the next point *[Tex \LARGE \left(1,-9\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-6,.1)),
  blue(circle(0,-6,.12)),
  blue(circle(0,-6,.15)),
  blue(circle(1,-9,.15,1.5)),
  blue(circle(1,-9,.1,1.5)),
  blue(arc(0,-6+(-3/2),2,-3,90,270)),
  blue(arc((1/2),-9,1,2, 0,180))
)}}}



Now draw a line through these points to graph {{{y=-3x-6}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,-3x-6),
  blue(circle(0,-6,.1)),
  blue(circle(0,-6,.12)),
  blue(circle(0,-6,.15)),
  blue(circle(1,-9,.15,1.5)),
  blue(circle(1,-9,.1,1.5)),
  blue(arc(0,-6+(-3/2),2,-3,90,270)),
  blue(arc((1/2),-9,1,2, 0,180))
)}}} So this is the graph of {{{y=-3x-6}}} through the points *[Tex \LARGE \left(0,-6\right)] and *[Tex \LARGE \left(1,-9\right)]



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


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim