Question 122153
You made a mistake in converting to slope-intercept form


"4y = 2x - 1" <--- In this step, it should be -2x since you subtract 2x from both sides



So the equation in slope-intercept form is



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






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



Since {{{b=-1/4}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-\frac{1}{4}\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,-\frac{1}{4}\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-1/4,.1)),
  blue(circle(0,-1/4,.12)),
  blue(circle(0,-1/4,.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 down 1  and over 2




So starting at *[Tex \LARGE \left(0,-\frac{1}{4}\right)], go down 1 unit 

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


and to the right 2 units to get to the next point *[Tex \LARGE \left(2,-\frac{5}{4}\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-1/4,.1)),
  blue(circle(0,-1/4,.12)),
  blue(circle(0,-1/4,.15)),
  blue(circle(2,-5/4,.15,1.5)),
  blue(circle(2,-5/4,.1,1.5)),
  blue(arc(0,-1/4+(-1/2),2,-1,90,270)),
  blue(arc((2/2),-5/4,2,2, 0,180))
)}}}



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


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,-(1/2)x-1/4),
  blue(circle(0,-1/4,.1)),
  blue(circle(0,-1/4,.12)),
  blue(circle(0,-1/4,.15)),
  blue(circle(2,-5/4,.15,1.5)),
  blue(circle(2,-5/4,.1,1.5)),
  blue(arc(0,-1/4+(-1/2),2,-1,90,270)),
  blue(arc((2/2),-5/4,2,2, 0,180))
)}}} So this is the graph of {{{y=-(1/2)x-1/4}}} through the points *[Tex \LARGE \left(0,-\frac{1}{4}\right)] and *[Tex \LARGE \left(2,-\frac{5}{4}\right)]