Question 195401
{{{12x-3y=24}}} Start with the given equation.



{{{-3y=24-12x}}} Subtract {{{12x}}} from both sides.



{{{-3y=-12x+24}}} Rearrange the terms.



{{{y=(-12x+24)/(-3)}}} Divide both sides by {{{-3}}} to isolate y.



{{{y=((-12)/(-3))x+(24)/(-3)}}} Break up the fraction.



{{{y=4x-8}}} Reduce.





Looking at {{{y=4x-8}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=4}}} and the y-intercept is {{{b=-8}}} 



Since {{{b=-8}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-8\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,-8\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-8,.1)),
  blue(circle(0,-8,.12)),
  blue(circle(0,-8,.15))
)}}}



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

{{{slope=rise/run}}}


Also, because the slope is {{{4}}}, this means:


{{{rise/run=4/1}}}



which shows us that the rise is 4 and the run is 1. This means that to go from point to point, we can go up 4  and over 1




So starting at *[Tex \LARGE \left(0,-8\right)], go up 4 units 

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-8,.1)),
  blue(circle(0,-8,.12)),
  blue(circle(0,-8,.15)),
  blue(arc(0,-8+(4/2),2,4,90,270))
)}}}


and to the right 1 unit to get to the next point *[Tex \LARGE \left(1,-4\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-8,.1)),
  blue(circle(0,-8,.12)),
  blue(circle(0,-8,.15)),
  blue(circle(1,-4,.15,1.5)),
  blue(circle(1,-4,.1,1.5)),
  blue(arc(0,-8+(4/2),2,4,90,270)),
  blue(arc((1/2),-4,1,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=4x-8}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,4x-8),
  blue(circle(0,-8,.1)),
  blue(circle(0,-8,.12)),
  blue(circle(0,-8,.15)),
  blue(circle(1,-4,.15,1.5)),
  blue(circle(1,-4,.1,1.5)),
  blue(arc(0,-8+(4/2),2,4,90,270)),
  blue(arc((1/2),-4,1,2, 180,360))
)}}} So this is the graph of {{{y=4x-8}}} through the points *[Tex \LARGE \left(0,-8\right)] and *[Tex \LARGE \left(1,-4\right)]