Question 202302


{{{x-2y=6}}} Start with the given equation.



{{{-2y=6-x}}} Subtract {{{x}}} from both sides.



{{{-2y=-x+6}}} Rearrange the terms.



{{{y=(-x+6)/(-2)}}} Divide both sides by {{{-2}}} to isolate y.



{{{y=((-1)/(-2))x+(6)/(-2)}}} Break up the fraction.



{{{y=(1/2)x-3}}} Reduce.




Looking at {{{y=(1/2)x-3}}} 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=-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 {{{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 up 1  and over 2




So starting at *[Tex \LARGE \left(0,-3\right)], go up 1 unit 

{{{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+(1/2),2,1,90,270))
)}}}


and to the right 2 units to get to the next point *[Tex \LARGE \left(2,-2\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(2,-2,.15,1.5)),
  blue(circle(2,-2,.1,1.5)),
  blue(arc(0,-3+(1/2),2,1,90,270)),
  blue(arc((2/2),-2,2,2, 180,360))
)}}}



Now draw a line through these points to graph {{{y=(1/2)x-3}}}


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  graph(500,500,-10,10,-10,10,(1/2)x-3),
  blue(circle(0,-3,.1)),
  blue(circle(0,-3,.12)),
  blue(circle(0,-3,.15)),
  blue(circle(2,-2,.15,1.5)),
  blue(circle(2,-2,.1,1.5)),
  blue(arc(0,-3+(1/2),2,1,90,270)),
  blue(arc((2/2),-2,2,2, 180,360))
)}}} So this is the graph of {{{y=(1/2)x-3}}} through the points *[Tex \LARGE \left(0,-3\right)] and *[Tex \LARGE \left(2,-2\right)]



Note: if you need more points, simply pick random x values to find the corresponding y values.