Treadline Analysis B17A0B

1. **Problem statement:** We have a treadline equation $$y = 11x - 12.3$$ and a correlation coefficient $$r = -0.9743$$. We want to find how much $$y$$ changes when $$x$$ increases by 1. 2. **Formula and explanation:** The treadline equation is in the form $$y = mx + b$$ where $$m$$ is the slope representing the change in $$y$$ for a unit increase in $$x$$. 3. **Step 1:** Identify the slope $$m$$ from the equation: $$m = 11$$ 4. **Step 2:** The slope $$m = 11$$ means that for every increase of 1 in $$x$$, $$y$$ increases by 11. --- 5. **Problem statement:** Based on the correlation coefficient $$r = -0.9743$$, determine if the points represent a line. 6. **Explanation:** The correlation coefficient $$r$$ measures the strength and direction of a linear relationship between $$x$$ and $$y$$. - $$r$$ ranges from $$-1$$ to $$1$$. - $$|r|$$ close to 1 indicates a strong linear relationship. - Negative $$r$$ means a negative slope, positive $$r$$ means positive slope. 7. **Step 1:** Here, $$r = -0.9743$$ which is very close to $$-1$$, indicating a strong negative linear relationship. 8. **Step 2:** However, the treadline slope is positive ($$11$$), which conflicts with the negative $$r$$. 9. **Step 3:** This suggests the treadline equation and $$r$$ do not correspond to the same data or there is an inconsistency. 10. **Conclusion:** Based on $$r$$ alone, the points strongly represent a line but with a negative slope. --- 11. **Problem statement:** Using the treadline equation $$y = 11x - 12.3$$, find $$y$$ when $$x = 20$$. 12. **Step 1:** Substitute $$x = 20$$ into the equation: $$y = 11(20) - 12.3$$ 13. **Step 2:** Calculate: $$y = 220 - 12.3 = 207.7$$ 14. **Final answer:** When $$x = 20$$, $$y = 207.7$$.