Question 369956
{{{y-3=(1/2)(x-5)}}} Start with the given equation.



{{{y-3=(1/2)x-(1/2)(5)}}} Distribute.



{{{y-3=(1/2)x-5/2}}} Multiply.



{{{y=(1/2)x-5/2+3}}} Add 3 to both sides.



{{{y=(1/2)x+1/2}}} Combine like terms.



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



Since {{{b=1/2}}} this tells us that the y-intercept is *[Tex \LARGE \left(0,\frac{1}{2}\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}{2}\right)]


{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,1/2,.1)),
  blue(circle(0,1/2,.12)),
  blue(circle(0,1/2,.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,\frac{1}{2}\right)], go up 1 unit 

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


and to the right 2 units to get to the next point *[Tex \LARGE \left(2,\frac{3}{2}\right)]

{{{drawing(500,500,-10,10,-10,10,
  grid(1),
  blue(circle(0,1/2,.1)),
  blue(circle(0,1/2,.12)),
  blue(circle(0,1/2,.15)),
  blue(circle(2,3/2,.15,1.5)),
  blue(circle(2,3/2,.1,1.5)),
  blue(arc(0,1/2+(1/2),2,1,90,270)),
  blue(arc((2/2),3/2,2,2, 180,360))
)}}}



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


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



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim