Question 141165


{{{x-4y=8}}} Start with the given equation



{{{-4y=8-x}}}  Subtract {{{ x}}} from both sides



{{{-4y=-x+8}}} Rearrange the equation



{{{y=(-x+8)/(-4)}}} Divide both sides by {{{-4}}}



{{{y=(-1/-4)x+(8)/(-4)}}} Break up the fraction



{{{y=(1/4)x-2}}} Reduce






Looking at {{{y=(1/4)x-2}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=1/4}}} 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 {{{1/4}}}, this means:


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



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




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 4 units to get to the next point *[Tex \LARGE \left(4,-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(4,-1,.15,1.5)),
  blue(circle(4,-1,.1,1.5)),
  blue(arc(0,-2+(1/2),2,1,90,270)),
  blue(arc((4/2),-1,4,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=(1/4)x-2}}}


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