Identify the differential equation that you will be using to create your slope field. Differential equations are usually expressed as equal to dy/dx or a derivative such as y' or f'(x). If you're given an equation in a different form, you may need to differentiate or integrate it first.
Draw a coordinate plane. Your plane should extend three to five points outward each direction on both the x-axis and y-axis. On tests, the coordinate plane will often be provided for you.
Plug coordinate points into the differential equation. Substitute the x-coordinate for x and the y-coordinate for y in the equation and solve for the numerical value. The solution is the slope of the equation at that point. For example, plugging in the point (1,1) to the equation dy/dx = x + y yields a solution of 2. Repeat this step for each coordinate on the plane.
Sketch the slope of the equation at each point on the coordinate plane. If the slope of the equation at (1,1) is 1, for example, draw a small line with a perfectly diagonal slope at the point (1,1). If the slope at (-1,1) is 0, draw a flat line at the point (-1,1). Repeat this step for each point on the coordinate plane. After each point on the plane has a slope, you have completed the slope field.