Question 70613
Given {{{-3x+y=6}}} 
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The slope intercept form of an equation is:
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{{{y = mx+b}}}
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where m represents the slope and b is the value of y where the graph crosses the y-axis.
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So to put the given equation into the slope intercept form, you need to have just y on the left
side and the x term plus a constant (that could be zero) on the right side. The first thing 
that is evident is that you need to get rid of the -3x on the left side.  Do this by adding
+3x to both sides.  The result is:
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{{{y = 3x+6}}}
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Note that this is exactly like the slope intercept form.  m is the 3 and b is the +6.
So you can put a dot on the y-axis at +6 because that is b and b is where the graph crosses
the y axis.  Next, the slope of +3 means that the graph rises 3 units for every 1 unit that
you move horizontally to the right.  You can draw this by putting your pencil on the dot you 
put on the y-axis at +6. Then move your pencil one horizontal unit to the right. Stop. Now move your 
pencil vertically up 3 units. Stop.  You should be at the point (1,9). Put a mark at that
point because it is on the graph.  From that point move horizontally 1 unit to the right. 
Stop your pencil. Then move vertically up 3 units. Stop your pencil and mark the point.  You 
should be at (2,12).  You now have 3 points on the graph. Put a straight edge along those points
and extend a line through them in both directions.  That is the graph of the equation.
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The reason you moved up after moving one unit to the right was because the slope was positive.
If the slope had been negative, then for every unit you moved your pencil horizontally
to the right you would then move vertically down a number of units equal to the slope.
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Hope this helps you understand the slope intercept form a little better.