← Unit 7: Differential Equations
Slope Fields
A slope field visualizes a differential equation dy/dx = f(x,y) by drawing short line segments with the correct slope at many grid points, letting you sketch solution curves without solving the equation.
Reading and sketching slope fields
At each point (x,y) on the grid, dy/dx = f(x,y) gives the slope of the tiny segment drawn there. A particular solution curve through a given point follows the flow of these segments — it must be tangent to every segment it passes through.
To match a slope field to its differential equation, test a few grid points: plug their (x,y) coordinates into candidate equations and see which one produces the slope drawn at that point.
Key terms (1)
- Slope field
- A grid of short segments showing the slope dy/dx = f(x,y) at many points, used to visualize solutions without solving the equation.
Practice Quiz
Question 1 of 2Score so far: 0/0
In a slope field for dy/dx = x, what should the segments look like along the y-axis (where x=0)?