1. **State the problem:** We are given four ordered pairs: (16, 18), (12, 12), (9, 10), and (3, 6). We need to find which one does not lie on the same line formed by the other three. 2. **Formula and approach:** To check if points lie on the same line, we can calculate the slope between pairs of points. The slope formula is: $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ If three points have the same slope between them, they are collinear. 3. **Calculate slopes between points:** - Slope between (3, 6) and (9, 10): $$\frac{10 - 6}{9 - 3} = \frac{4}{6} = \frac{2}{3}$$ - Slope between (9, 10) and (12, 12): $$\frac{12 - 10}{12 - 9} = \frac{2}{3}$$ - Slope between (12, 12) and (16, 18): $$\frac{18 - 12}{16 - 12} = \frac{6}{4} = \frac{3}{2}$$ 4. **Analyze slopes:** The first two slopes are both $\frac{2}{3}$, but the slope between (12, 12) and (16, 18) is $\frac{3}{2}$, which is different. 5. **Check if (16, 18) fits the line with slope $\frac{2}{3}$:** Using point-slope form with point (3, 6): $$y - 6 = \frac{2}{3}(x - 3)$$ Plug in $x=16$: $$y - 6 = \frac{2}{3}(16 - 3) = \frac{2}{3} \times 13 = \frac{26}{3} \approx 8.67$$ $$y = 6 + 8.67 = 14.67$$ But the point is (16, 18), so $y=18 \neq 14.67$. 6. **Conclusion:** The point (16, 18) does not lie on the line formed by the other three points. **Final answer:** (16, 18) does not fall on the line formed by the other three.