Question 317810


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



Since {{{b=1}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,1\right)].Remember the y-intercept is the point where the graph intersects with the y-axis


So we have one point *[Tex \LARGE \left(0,1\right)]


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



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

{{{slope=rise/run}}}


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


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



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




So starting at *[Tex \LARGE \left(0,1\right)], go down 2 units 

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


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

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



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


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




Since you can plug in any x value, this means that the domain is the set of all real numbers.



Because you can plug in any number, you can effectively land on any number in the range. So the range is also the set of all real numbers.