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Warm Up

Warm Up. 7.1 B – Slope Fields. Goal: draw a slope field, and match a slope field to an appropriate equation . Slope Fields.

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Warm Up

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  1. Warm Up

  2. 7.1 B – Slope Fields • Goal: draw a slope field, and match a slope field to an appropriate equation

  3. Slope Fields Slope fields are mostly used as a learning tool and are mostly done on a computer or graphing calculator, but recent AP tests have asked students to draw a simple one by hand. • Slope fields can help us produce the family of curves that satisfies a differential equation. • Remember: Differential equations give the slope at any point (x, y), and this information can be used to draw a small piece of the linearization at that point, which approximates the solution curve that passes through that point. This process will be repeated for several points to produce a slope field.

  4. How do we do it? • To make a slope field, plug in coordinate points for x and y and see what the slope is. • Then, draw a tiny line segment with that slope at that point. • You will see patterns allowing you to get an idea of the what the original function is.

  5. Draw a segment with slope of 2. Draw a segment with slope of 0. Draw a segment with slope of 4. 0 0 0 0 1 0 0 2 0 0 3 0 2 1 0 1 1 2 2 0 4 -1 -2 0 0 -4 -2

  6. If you know an initial condition, such as (1,-2), you can sketch the particular curve. By following the slope field, you get a rough picture of what the curve looks like. In this case, it is a parabola.

  7. Try another

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