Substitute an equal sign for the inequality sign. The resulting equation will give us the equation for the boundary of the region that represents the graph of the inequality.
Get rid of the fractions. This is accomplished by multiplying throughout by the product of the denominators of the fractions. It is often possible to simplify the resulting equation by dividing out any common factors. For example, if X/6 - Y/15 = 1/2, we can multiply through by the product of the denominators -- 6 X 15 = 90 -- to get 15X - 6Y = 45. Now 3 is a common factor so dividing the equation throughout by 3 we get 5X - 2Y = 15. This equation has the same graph as the original equation but will be much easier to work with.
Choose a point that is clearly on one side of the boundary line. Plug this point into the inequality and see if it makes the inequality true or false. If the point makes the inequality true, all the points on the same side of the boundary as the point you chose are in the region of the graph. If the point you chose makes the inequality false, all the points on the other side of the boundary from the point you chose represent the graph of the inequality. For example, if the inequality is X/6 - Y/15 is-less-than 1/2. Substituting the point (0, 0) into the inequality gives 0 - 0 is-less-than 1/2 which is true. This means that the region that is on the same side of the 5X - 2Y = 15 boundary line represents the graph of the inequality.