Draw a Cartesian plane. A Cartesian plane is the intersection of a vertical line with a horizontal line. Use a ruler to measure out your Cartesian plane so that the X and Y axes are the same length. Draw a scale along the X and Y axes; if the equation you are working with contains figures in the 100s, draw the scale in increments of 100; if the equation you are working with contains figures in the 1000s, draw the scale in increments of 1000.
Read the supply and demand equations for the model. Ask yourself whether one or both of the equations can be graphed directly, or whether the equations need to be rearranged. If a graph reads "Y = 300 + 1/4q1", you do not need to rearrange it. If it reads "q1 = 300 + 4Y", you need to rearrange it so that the Y is on the left side of the equation.
Rearrange any equations that need to be rearranged. In order to graph a model, you need to get the figure for the Y axis (usually just "Y", sometimes "P") alone on the left side of the equation. To isolate the Y or P figure, put the figure that Y is being multiplied/divided by, or added/subtracted to, on the other side of the equation. Any figure that is added on one side of the equation, subtract it when you put it on the other side of the equation. Any figure that is multiplied on one side of the equation, divide it on the other side of the equation. The same rules apply for the reverse operations.
Find the Y intercept of the graph. The Y intercept of a function is the part that is added or subtracted to "P/Q" or "P/X" part of the function. For example, in the equation "Y = 400 + 1/4Q", 400 is the Y intercept. Place a visible dot on the number on the Y axis of your graph that corresponds to the Y intercept. For example, if your Y intercept is 300, put a dot on the 300 point on your Y axis.
Draw the graph. Look at the part of your function that is divided by or multiplied by "X" or "Q". Use the numerator (top number) of the fraction to determine how far to the right the next point will be, and use the denominator (lower number) to determine how far up or down the next point will be. For example, if the fraction is "1/4 Q", draw the next point one space to the right and four spaces up from the Y intercept. If X is multiplied by an integer, as in "2x", simply move up one square and to the right one square from the Y intercept. Draw a line to connect these points when you have gone all the way to the top or the right of the graph.