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 = <em>-3/2</em> x <em>+</em><em>3</em>
This is the form you want. Just looking at it, it tells you that the slope of the line on the graph is (<em>-3/2</em>), and it crosses the y-axis at <em>+3</em> . 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: <u>3x + 2y = 6 .</u>
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.
