Answer :

jtgbama
Plot these coordinates then draw a line through them and that is the line.

(2,0) x intercept
(0,3) y intercept
AL2006

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.
===============================================

=>  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.


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