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7.3 Sketching Slope Fields

1 min readβ€’october 19, 2021

Jacob Jeffries

Jacob Jeffries


AP Calculus AB/BC ♾️

279Β resources
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Slope Fields

Slope fields allow us to visualize a solution to a differential equation without actually solving the differential equation. Let’s construct a slope field to solidify this idea. 🧠
Slope fields essentially draw the slopes of line segments that go through certain points. Let’s consider the following differential equation:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(931).png?alt=media&token=7639fd09-c6ef-42fb-aaea-50fdba7cb745
The slope (m) at point (x, y), in this case, is just x + y, which we can put into a table for various coordinates:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(932).png?alt=media&token=3c8b9a1e-545c-443e-a283-f65932e751e4
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: πŸŒ„
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(933).png?alt=media&token=c1fa6f93-c2c6-45be-bce8-4798f4bdba14
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πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
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