Question: 7.3: Sketching Slope Fields

Answer:

Question: A slope field

Answer: A plot of short line segments with slopes f(x,y) at lattice points (x,y) in the plane.

Question: A slope field represents

Answer: a differential equation on an xy-plane.

Question: What does a slope field show

Answer: the “slope” of all the particular solutions to the differential equation

Question: Slope field

Answer: plug (x,y) coordinates into differential equation

draw short segments representing slope at each point