Question 111519
To get the slope intercept form, you need to solve the equation for y, in other words put it into the form {{{y=mx+b}}}
:
{{{3x-6y=9}}}
{{{-6y=-3x+9}}}
{{{y=(1/2)x-3/2}}}
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Now you know the slope is 1/2 and the y-intercept is -3/2
:
To graph it, you only need to plot two points.  One of the points is given by the y-intercept, that is, you know the line passes through (0,-3/2).  Pick a second value for x.  Let's pick 1.  Then at x = 1, y = 1/2 - 3/2 = -1, so the second point is (1, -1).
:
Plot the two points and connect them with a straight line.  It should look like this:
:
{{{graph(400,400,-3,3,-3,3,(1/2)x-3/2)}}}