1. 6.1 Slope Fields

2. I. Example-
Find the equation of the line tangent to the circle given below at the point (3,4).
Does the radius matter in finding ?

3. II. The Slope Field
A plot of short line segments with slopes f(x,y) for a lattice of points (x,y) in the plane.

4. III. Examples
See Overhead -

5. IV. Making a Slope Field
1.) Short, straight line segments NO TOUCHING!!
2.) Slopes must vary according to “steepness”

6. V. Reading a Slope Field 1.) Look for slopes equal to 0 or undefined.
2.) look at the slopes along the x and y axes.
3.) See if the slope depends on the value of x or y or both.
4.) See where the slopes are positive (function increasing) or negative (function decreasing).

7. VI. Types of Problems on the AP
GIVEN CHOOSE
1.) diff. eq. Slope field
2.) solution fn. Slope field
3.) slope field diff. eq.
4.) slope field solution fn.

8. VI. Examples
See Handout – work in groups – Slope field WS packet due next THURSDAY!!!