1. **State the problem:** We are given two points A(0,-2) and B(-4,0) and need to find which equation matches the graph passing through these points. 2. **Recall the formula:** A line equation can be written as $Ax + By = C$. To check if a line passes through points, substitute the points into the equation and verify if the equality holds. 3. **Check option (a) $y = x + 3$:** - For point A(0,-2): Substitute $x=0$, $y=-2$ into $y = x + 3$ gives $-2 = 0 + 3 = 3$, which is false. 4. **Check option (b) $x - 2 + y$ (incomplete, but assuming $x - 2 + y = 0$):** - For point A(0,-2): Substitute $x=0$, $y=-2$ gives $0 - 2 + (-2) = -4 eq 0$, false. 5. **Check option (c) $x + 2y = -4$:** - For point A(0,-2): $0 + 2(-2) = 0 - 4 = -4$, true. - For point B(-4,0): $-4 + 2(0) = -4 + 0 = -4$, true. 6. Since both points satisfy $x + 2y = -4$, this is the correct equation. 7. **Simplify for $y$:** $$x + 2y = -4$$ $$2y = -4 - x$$ $$y = \frac{-4 - x}{2} = -2 - \frac{x}{2}$$ **Final answer:** The equation matching the graph is $x + 2y = -4$.