Slope Field Example

AP Calculus · Axiom Academy

Matching a differential equation to its slope field x - y = 0 means y = x . Along this line, all slopes are horizontal. At (0,1) : slope = -1 (going down). The curve dips below y = x , then bends back toward the line y = x - 1 as an equilibrium-like attractor. The exact solution is y = x - 1 + 2e^ -x , which starts at y(0) = 1 and approaches y = x - 1 as . Where is the slope zero in the field for dy/dx = x - y ? You've worked through the full solution. Review each step to solidify your understanding.

This is the written version of the interactive lesson above. See the full AP Calculus course.