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7.3 Sketching Slope Fields

Jacob Jeffries

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Slope Fields

Slope fields allow us to visualize a solution to a differential equation without actually solving the differential equation. Letβs construct a slope field to solidify this idea. π§
Slope fields essentially draw the slopes of line segments that go through certain points. Letβs consider the following differential equation:
The slope (m) at point (x, y), in this case, is just x + y, which we can put into a table for various coordinates:
We can use this data to draw an approximate solution to the differential equation by drawing short line segments through each point that have the corresponding slope: π
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