Slope Field Problems

Slope field questions are usualy part of one of the the problems of the free response section. In most cases, a differential equation is given, dy/dx = f(x, y), and the student is asked to sketch the slope field at a specific set of points. The slope of the line at a specific point, (x₀, y₀) is f(x₀, y₀).
Your sketch has to reflect the sign of the slope at each point and the relative steepness of slope lines. Example.

Example of slope field question

1.2. dy/dx = (x + 1)²y
Sketch a slope field for the given differential equation at the points indicated.

Solution: Calculate dy/dx for each point. For example, for (1, 2), dy/dx = (1 + 1)²2 = 8.