Question 926179
Solve for y.



{{{26x - 13y = 39}}}



{{{-13y = 39-26x}}}



{{{-13y = -26x+39}}}



{{{y = (-26x+39)/(-13)}}}



{{{y = (-26x)/(-13)+(39)/(-13)}}}



{{{y = 2x-3}}}



Slope is m = 2 and y intercept is b = -3. The y intercept as a point is (0,-3)



Let's graph.



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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 up 2  and over 1




So starting at *[Tex \LARGE \left(0,-3\right)], go up 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, 180,360))
)}}}



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,-10,10,0,2x-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))
)}}} 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)]
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