1. **State the problem:** We have 5 points A(-3,4), B(-3,8), C(0,12), D(3,8), and E(3,8) on a petal and want to find the equation of the line passing through these points. 2. **Check if points lie on the same line:** To write the equation of a line, points must be collinear. We check slopes between pairs. 3. **Calculate slope between A and B:** $$m = \frac{8 - 4}{-3 - (-3)} = \frac{4}{0}$$ Slope is undefined (vertical line) between A and B. 4. **Calculate slope between B and C:** $$m = \frac{12 - 8}{0 - (-3)} = \frac{4}{3}$$ Slope is $\frac{4}{3}$. 5. **Calculate slope between C and D:** $$m = \frac{8 - 12}{3 - 0} = \frac{-4}{3}$$ Slope is $-\frac{4}{3}$. 6. **Calculate slope between D and E:** $$m = \frac{8 - 8}{3 - 3} = \frac{0}{0}$$ Slope is undefined but points D and E are the same point. 7. **Conclusion:** Points are not collinear; they do not lie on a single straight line. 8. **Find equations of vertical lines through A and B:** Since A and B have $x = -3$, equation is: $$x = -3$$ 9. **Find equation of line through C and D:** Using point-slope form with point C(0,12) and slope $-\frac{4}{3}$: $$y - 12 = -\frac{4}{3}(x - 0)$$ Simplify: $$y = -\frac{4}{3}x + 12$$ 10. **Find equation of vertical line through D and E:** Since D and E have $x = 3$, equation is: $$x = 3$$ **Final answer:** The points lie on three lines: - Vertical line $x = -3$ through A and B - Line $y = -\frac{4}{3}x + 12$ through C and D - Vertical line $x = 3$ through D and E