AP Calculus AB / Unit 7: Differential Equations
7.3 Sketching Slope Fields
Notes
A slope field draws short segments with slope $\displaystyle \frac{dy}{dx}$ at grid points.
- Plug each point $(x,y)$ into the equation to get its slope.
- Where $\displaystyle \frac{dy}{dx}=0$, segments are horizontal.
Practice
For $\displaystyle \frac{dy}{dx}=x-y$, the slope at $(2,1)$ is:
$2-1$.
For $\displaystyle \frac{dy}{dx}=y$, segments are horizontal along:
Slope is 0 when $y=0$.
For $\displaystyle \frac{dy}{dx}=x^2$, segments in the same column (same $x$) are:
Slope depends only on $x$.
Ready for more? Take the Unit 7 test.