1. **State the problem:** We are given the equation $2x + y = 4$ and a point $(3, -2)$. We want to check if the point satisfies the equation. 2. **Recall the rule:** To check if a point $(x, y)$ lies on the line given by an equation, substitute the $x$ and $y$ values into the equation and see if the equality holds. 3. **Substitute the point into the equation:** $$2(3) + (-2) = 6 - 2 = 4$$ 4. **Evaluate:** Since the left side equals the right side ($4 = 4$), the point $(3, -2)$ lies on the line $2x + y = 4$. **Final answer:** The point $(3, -2)$ satisfies the equation $2x + y = 4$.