Question 181937


Looking at {{{y=-2x+3}}} 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=3}}} 



Since {{{b=3}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,3\right)].Remember the y-intercept is the point where the graph intersects with the y-axis


So we have one point *[Tex \LARGE \left(0,3\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,3,.1)),
  blue(circle(0,3,.12)),
  blue(circle(0,3,.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(0,3\right)], go down 2 units 

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,3,.1)),
  blue(circle(0,3,.12)),
  blue(circle(0,3,.15)),
  blue(arc(0,3+(-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(0,3,.1)),
  blue(circle(0,3,.12)),
  blue(circle(0,3,.15)),
  blue(circle(1,1,.15,1.5)),
  blue(circle(1,1,.1,1.5)),
  blue(arc(0,3+(-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+3}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,-2x+3),
  blue(circle(0,3,.1)),
  blue(circle(0,3,.12)),
  blue(circle(0,3,.15)),
  blue(circle(1,1,.15,1.5)),
  blue(circle(1,1,.1,1.5)),
  blue(arc(0,3+(-2/2),2,-2,90,270)),
  blue(arc((1/2),1,1,2, 0,180))
)}}} So this is the graph of {{{y=-2x+3}}} through the points *[Tex \LARGE \left(0,3\right)] and *[Tex \LARGE \left(1,1\right)]



Now notice that the graph extends in both directions along the x-axis. So this means that ANY value of "x" can be plugged into the function. 


So the domain is all real numbers.



Also, take note that the graph extends in both directions along the y-axis as well. So this tells us that the range is also ANY number.


So the range is all real numbers.