Question 139503

{{{3x-2y=-18}}} Start with the given equation



{{{-2y=-18-3x}}}  Subtract {{{3 x}}} from both sides



{{{-2y=-3x-18}}} Rearrange the equation



{{{y=(-3x-18)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=(-3/-2)x+(-18)/(-2)}}} Break up the fraction



{{{y=(3/2)x+9}}} Reduce





Looking at {{{y=(3/2)x+9}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=3/2}}} and the y-intercept is {{{b=9}}} 



Since {{{b=9}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,9\right)].Remember the y-intercept is the point where the graph intersects with the y-axis


So we have one point *[Tex \LARGE \left(0,9\right)]


{{{drawing(500,500,-10,10,-5,15,
  grid(1),
  blue(circle(0,9,.1)),
  blue(circle(0,9,.12)),
  blue(circle(0,9,.15))
)}}}



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

{{{slope=rise/run}}}


Also, because the slope is {{{3/2}}}, this means:


{{{rise/run=3/2}}}



which shows us that the rise is 3 and the run is 2. This means that to go from point to point, we can go up 3  and over 2




So starting at *[Tex \LARGE \left(0,9\right)], go up 3 units 

{{{drawing(500,500,-10,10,-5,15,
  grid(1),
  blue(circle(0,9,.1)),
  blue(circle(0,9,.12)),
  blue(circle(0,9,.15)),
  blue(arc(0,9+(3/2),2,3,90,270))
)}}}


and to the right 2 units to get to the next point *[Tex \LARGE \left(2,12\right)]

{{{drawing(500,500,-10,10,-5,15,
  grid(1),
  blue(circle(0,9,.1)),
  blue(circle(0,9,.12)),
  blue(circle(0,9,.15)),
  blue(circle(2,12,.15,1.5)),
  blue(circle(2,12,.1,1.5)),
  blue(arc(0,9+(3/2),2,3,90,270)),
  blue(arc((2/2),12,2,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=(3/2)x+9}}}


{{{drawing(500,500,-10,10,-5,15,
  grid(1),
  graph(500,500,-10,10,-5,15,(3/2)x+9),
  blue(circle(0,9,.1)),
  blue(circle(0,9,.12)),
  blue(circle(0,9,.15)),
  blue(circle(2,12,.15,1.5)),
  blue(circle(2,12,.1,1.5)),
  blue(arc(0,9+(3/2),2,3,90,270)),
  blue(arc((2/2),12,2,2, 180,360))
)}}} So this is the graph of {{{y=(3/2)x+9}}} through the points *[Tex \LARGE \left(0,9\right)] and *[Tex \LARGE \left(2,12\right)]