7.3 Sketching Slope Fields

What a slope field is

A slope field draws short segments at grid points, each with slope equal to dy/dx there. It's a visual picture of a differential equation.

Building one

At each point, evaluate dy/dx and draw a small segment of that slope. For dy/dx = x + y at (1, 1), the slope is 2. Solution curves follow the flow of the segments.

Key terms

Slope field

Short segments showing dy/dx at grid points.

Segment slope

Equals dy/dx at that point.

Solution curves

Follow the flow of the segments.

Building one

Evaluate dy/dx at each point and draw a segment.

Represents

A differential equation, visually.

Try an AP-style question

For dy/dx = x + y, what is the slope segment at (1, 2)?

1. −1
2. 1
3. 2
4. 3