Here are two ways to graph it. You can decide which one seems easier to understand or easier to do:
==> Manipulate the equation into the "slope-intercept" form, where 'y' is
all alone on one side and everything else is on the other side:
3x + 2y = 6
Subtract 3x from each side: 2y = -3x + 6
Divide each side by 2 : y = -3/2 x + 3
This is the form you want. Just looking at it, it tells you that the slope
of the line on the graph is (-3/2), and it crosses the y-axis at +3 .
That's enough information to draw the line.
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=> Another way:
Look at the x-axis and the y-axis on the graph paper ... without any graph drawn on it yet. Just look at the 2 axes.
With an 'x'-number and a 'y'-number, you can find any point on it. Right ?
OK. Notice that at every point on the y-axis, x = 0 . And at every point
on the x-axis, y = 0. This can be very very helpful.
Now take your equation: 3x + 2y = 6 .
You know that the graph is going to be a straight line. And it's pretty obvious that if the line isn't horizontal or vertical, then it has to cross both the x-axis and the y-axis somewhere. If you had an easy way to find the two points where it crosses the axes, you could join those 2 points and you'd have your line !
You DO have an easy way to find those points !
If x=0, then the point is on the y-axis. Take your equation, make x=0, and it'll show you where the line crosses the y-axis:
3(0) + 2y = 6 .
2y = 6 .
Divide each side by 2 : y = 3 .
There's one point on the line: (0, 3)
Now remember that if y=0 the point is on the x-axis. So take your equation
and make y=0:
3x + 2(0) = 6
3x = 6
Divide each side by 3 : x = 2
There's another point on the line, where it crosses the x-axis: (2, 0) .
Shazam ! You have the 2 points where the line crosses the x- and
y- axes. Mark each one with a little dot, put your ruler down along
them, draw a line between them, and extend it as far in each direction
as you want to. That's the graph of your equation.