A direction field (or slope field / vector field) is a picture of the general solution to a first order differential equation with the form

Edit the gradient function in the input box at the top. The function you input will be shown in blue underneath as

The Density slider controls the number of vector lines.

The Length slider controls the length of the vector lines.

Adjust and to define the limits of the slope field.

Check the Solution boxes to draw curves representing numerical solutions to the differential equation.

Click and drag the points A, B, C and D to see how the solution changes across the field.

Change the Step size to improve or reduce the accuracy of solutions (0.1 is usually fine but 0.01 is better).
If anything messes up....hit the reset button to restore things to default.