Question 157855


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



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



{{{4y=-x+8}}} Rearrange the terms.



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



{{{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 down 1  and over 4




So starting at *[Tex \LARGE \left(0,2\right)], go down 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, 0,180))
)}}}



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, 0,180))
)}}} 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)]