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## AP®︎/College Calculus BC

### Unit 7: Lesson 3

Sketching slope fields

# Worked example: slope field from equation

AP.CALC:
FUN‑7 (EU)
,
FUN‑7.C (LO)
,
FUN‑7.C.1 (EK)
Given a differential equation in x and y, we can draw a segment with dy/dx as slope at any point (x,y). That's the slope field of the equation. See how we match an equation to its slope field by considering the various slopes in the diagram.

## Want to join the conversation?

• what are some applications of slope fields and how is this math used in them ?
• Slopes fields are commonly used in physics and engineering....they can also be used in biology and other life-science disciplines....For instance, they are adopted to describe predator-prey interactions! They predict how the growth rate of prey changes based on varying levels of predator population......
• So a slope is basically a cartesian plane or a graph which shows what the derivative of a graph would look like at every point on that plane? If that is true then what is the point of a slope field if you can just use the separation of variables technique to solve any differential equation?
• Only a tiny subset of differential equations can be solved by separation of variables. The slope field gives us a way to visualize and work with differential equations even if we can't solve them explicitly.