Question 202449
{{{5x-10y=20}}} Start with the given equation.



{{{-10y=20-5x}}} Subtract {{{5x}}} from both sides.



{{{-10y=-5x+20}}} Rearrange the terms.



{{{y=(-5x+20)/(-10)}}} Divide both sides by {{{-10}}} to isolate y.



{{{y=((-5)/(-10))x+(20)/(-10)}}} Break up the fraction.



{{{y=(1/2)x-2}}} Reduce.





Looking at {{{y=(1/2)x-2}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=1/2}}} and the y-intercept is {{{b=-2}}} 



Since {{{b=-2}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-2\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,-2\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-2,.1)),
  blue(circle(0,-2,.12)),
  blue(circle(0,-2,.15))
)}}}



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

{{{slope=rise/run}}}


Also, because the slope is {{{1/2}}}, this means:


{{{rise/run=1/2}}}



which shows us that the rise is 1 and the run is 2. This means that to go from point to point, we can go up 1  and over 2




So starting at *[Tex \LARGE \left(0,-2\right)], go up 1 unit 

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


and to the right 2 units to get to the next point *[Tex \LARGE \left(2,-1\right)]

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



Now draw a line through these points to graph {{{y=(1/2)x-2}}}


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