2y-x=6
7x+3=-2y=3
y=1/2x-4
These are all lines. Do you know the "slope-intercept" form? We want to solve these equations to the form:
$\displaystyle y = mx + b$
Let's take the first one:
$\displaystyle 2y - x = 6$
We want to solve for y.
$\displaystyle 2y = x + 6$
$\displaystyle y = \frac{1}{2}x + 3$
Now, the constant at the end (the 3) represents the "y-intercept." This is the point where the line and the y-axis meet. It is the point (0, 3), so we know that this point is on our line.
Now, the coefficient of the x term (the 1/2) is called the "slope." It measures how fast the line is going up or down relative to an increase in x. What the 1/2 tells us is that if we start at a point on the line, say (0, 3), if we go up one unit and two units to the right we have another point on the line. So (2, 4) is also on our line.
Similarly (4, 5) is on the line, (6, 6) etc.
We can also go the other direction. The slope 1/2 means that if we go down one unit and go two units to the left we get another point on the line. So if we start at (0, 3), we know that (-2, 2) is on the line, (-4, 1) is on the line, etc.
So we have a bunch of points we can plot. Now we connect all of those dots with a straight line and we are done.
I have attached a graph of the first line. See what you can do for the other two.
-Dan