1. The problem provides a set of points $(x, y)$: $(0,0)$, $(1,-2)$, $(2,-4)$, and $(3,-6)$. 2. We want to find the equation of the line that fits these points. 3. Notice that as $x$ increases by 1, $y$ decreases by 2, indicating a linear relationship with slope $m = \frac{\Delta y}{\Delta x} = \frac{-2}{1} = -2$. 4. Using the point-slope form $y = mx + b$, substitute $m = -2$ and use the point $(0,0)$ to find $b$: $$0 = -2 \times 0 + b \implies b = 0$$ 5. Therefore, the equation of the line is: $$y = -2x$$ 6. This equation fits all given points exactly. Final answer: $y = -2x$