Gather the given information. To calculate the position of a point, you will need an equation that includes two variables, x and y, and a given value for one of those variables. This example will use an equation, y = 1/2x + 1, and a value, x = 4.
Plug the given value into the equation. From our example, if we plug x = 4 into the given equation, we get y = 1/2 x 4 + 1.
Solve the equation for the variable not given. In the case of the example, we will solve for y. If we do the arithmetic, this will give us the solution y = 3. The point that we must plot then is written (4, 3), with the x value first and the y second separated by a comma, inside parenthesis.
Draw a line horizontally across the paper, using the ruler as a straightedge. Label it "x axis." Turn the ruler 90 degrees and draw a line perpendicular to the first, intersecting roughly in the middle of the first, and label it "y axis." Where these two lines meet is called the origin. Draw tick marks every 1/8 inch or so from the origin in both directions on both lines. Cap the end of each line with an arrow shape.
Plot the point. From our example, the point we must plot is (4, 3). Count four of the small lines along the x axis to the right of the origin, and from that point, count three lines up on the y axis. Draw a small dot at this point. This is the x and y position of the graph at this point.