A graph represents a set of values that solve a given equation. Lets look at this equation.

When you solve this equation for "x" we find it equal to 4. Now what if there were two variables in the equation: y = 3/2x + 2. There is no single answer to this equation as there was in the last. For every value used for x there will be a different value of y. Literally there is an infinite number of solutions to this equation. The solution to this equation is no longer a single value but represented by a graph of all possible values.

The arrows show that this line continues infinitely in both directions. The x axis represents a possible value of x in the equation. the y axis represents a possible value of y in the equation. If you were to follow a straight line, from and perpendicular to the x axis, to the line formed by the equation till you intersect it you can find the resulting y value. From the intersection, if you were to continue to the y-axis you would find the exact value of y when x is a given number.

Each point along the line on the graph can be represented by a coordinate, (x,y), which also represents a set of solutions to the equation.

The equation y = 3/2x + 2 has various parts.  

The slope of a line defines the steapness of the line relative to the x-axis. The slope of the line is the coefficient of x when the equation of the line is in slope intercept form. The slope can be thought of as rise over run.

Therefore in the equation y = 3/2x + 2 has a slope of 3/2 illustrated below:

You should note that the slope runs from bottom left to the top right. If the slope was negative the orientation would be reversed running from top left to bottom right. So the graph of y = -3/2x + 2 is:

In this case the rise is negative so you go in the opposite direction. Instead of counting up 3 and over 2 as you did with the slope of 3/2 you count down 3 and over 2 for a slope of -3/2.

How is the slope found? You can't always easily see the rise over run. The slope of a line can be found when given any two points on a line using the slope equation:

In the equation we have been using, y = 3/2x + 2, the number after the addition sign represents the point along the y-axis where the line of the graph intercepts the y-axis. This number can be negative.

With these two pieces of information you can draw your graph.