Question 144016
Do you want to graph?





{{{4x-5y=4}}} Start with the given equation



{{{-5y=4-4x}}}  Subtract {{{4 x}}} from both sides



{{{-5y=-4x+4}}} Rearrange the equation



{{{y=(-4x+4)/(-5)}}} Divide both sides by {{{-5}}}



{{{y=(-4/-5)x+(4)/(-5)}}} Break up the fraction



{{{y=(4/5)x-4/5}}} Reduce





Looking at {{{y=(4/5)x-4/5}}} we can see that the equation is in slope-intercept form {{{y=mx+b}}} where the slope is {{{m=4/5}}} and the y-intercept is {{{b=-4/5}}} 



Since {{{b=-4/5}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,-\frac{4}{5}\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{4}{5}\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-4/5,.1)),
  blue(circle(0,-4/5,.12)),
  blue(circle(0,-4/5,.15))
)}}}



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

{{{slope=rise/run}}}


Also, because the slope is {{{4/5}}}, this means:


{{{rise/run=4/5}}}



which shows us that the rise is 4 and the run is 5. This means that to go from point to point, we can go up 4  and over 5




So starting at *[Tex \LARGE \left(0,-\frac{4}{5}\right)], go up 4 units 

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


and to the right 5 units to get to the next point *[Tex \LARGE \left(5,\frac{16}{5}\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,-4/5,.1)),
  blue(circle(0,-4/5,.12)),
  blue(circle(0,-4/5,.15)),
  blue(circle(5,16/5,.15,1.5)),
  blue(circle(5,16/5,.1,1.5)),
  blue(arc(0,-4/5+(4/2),2,4,90,270)),
  blue(arc((5/2),16/5,5,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=(4/5)x-4/5}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,(4/5)x-4/5),
  blue(circle(0,-4/5,.1)),
  blue(circle(0,-4/5,.12)),
  blue(circle(0,-4/5,.15)),
  blue(circle(5,16/5,.15,1.5)),
  blue(circle(5,16/5,.1,1.5)),
  blue(arc(0,-4/5+(4/2),2,4,90,270)),
  blue(arc((5/2),16/5,5,2, 180,360))
)}}} So this is the graph of {{{y=(4/5)x-4/5}}} through the points *[Tex \LARGE \left(0,-\frac{4}{5}\right)] and *[Tex \LARGE \left(5,\frac{16}{5}\right)]