Subjects algebra

Inverse Variation 969E1D

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1. **State the problem:** We are given points on a graph that show the relationship between Height and Width, described by the equation $$\text{Height} = \text{Constant} \times \text{Width}$$. We need to find the value of the constant. 2. **Formula and explanation:** The equation represents a direct variation where Height varies directly with Width. The constant is the ratio of Height to Width for any point on the line. 3. **Calculate the constant using the points:** - Using point (0.5, 1): $$\text{Constant} = \frac{\text{Height}}{\text{Width}} = \frac{1}{0.5} = 2$$ - Using point (2, 4): $$\text{Constant} = \frac{4}{2} = 2$$ - Using point (3, 6): $$\text{Constant} = \frac{6}{3} = 2$$ - Using point (5, 10): $$\text{Constant} = \frac{10}{5} = 2$$ 4. **Conclusion:** Since the constant is the same for all points and equals 2, the constant in the equation is 2. **Final answer:** 2