Slope Fields

Slope fields are a way to visualize the family of solutions for a differential equation. This concept relates directly to finding an indefinite integral, and how the solution to the indefinite integral has a family of solutions that you acknowledge exists when you put that +C at the end of the solution.

Remember that a differential equation is an equation for finding slopes. You really want to use the given differential equation to find the slope at different easy to find points, ( x , y ). This is really going all the way back to our derivative triangle and the value of the slope.