Method 2: Sketching a Slope Field

Step 1: Choose any one of the given points, ( x , y ),  marked by a black dot on your given x–y axis.

Step 2: Plug the values from the point you selected in Step 1 into your given differential equation, ${\left.\frac{\mathit{dy}}{\mathit{dx}}\right|}_{(x,y)}$.

Step 3: Use the value you found for the slope in Step 2 to sketch a short line with that slope at the point you chose in Step 1 .

Repeat these steps as much as needed to sketch as many slope curves as required by your problem.