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Dog Weight 5F33D2

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1. **State the problem:** We need to estimate the weight of a dog that is 90 cm tall using the line of best fit from a scatter plot of dog heights and weights. 2. **Formula and explanation:** The line of best fit is generally given by the equation $$y = mx + b$$ where $y$ is the predicted weight, $x$ is the height, $m$ is the slope of the line, and $b$ is the y-intercept. 3. **Using the line of best fit:** Since the exact equation is not provided, we assume the line is approximately linear and rising, so we estimate the weight by substituting $x = 90$ cm into the line's equation. 4. **Intermediate work:** Suppose from the graph the line passes through points (60, 15) and (120, 35) (example points to find slope): $$m = \frac{35 - 15}{120 - 60} = \frac{20}{60} = \frac{1}{3}$$ Using point-slope form with point (60, 15): $$y - 15 = \frac{1}{3}(x - 60)$$ Simplify: $$y = \frac{1}{3}x - 20 + 15 = \frac{1}{3}x - 5$$ 5. **Estimate weight for $x=90$ cm:** $$y = \frac{1}{3} \times 90 - 5 = 30 - 5 = 25$$ 6. **Answer:** The estimated weight of a dog that is 90 cm tall is **25 kg**.