Question: User: x\ty 2\t82 4\t74 6\t63 8\t50 10\t42 12\t31 Treadline: y = -5.2x + 93.4 r= -0.9981 1. How much does y change when x increases by 1? 2. Based on r, do these points represent a line? 3. Using the treadline equation, what should y equal if x is 20? Graph shape: a scatter plot/table of points showing a strong negative linear relationship, located top-left; the fitted line is decreasing from left to right with equation y = -5.2x + 93.4 and correlation r = -0.9981.

1. **State the problem:** We want to find how much $y$ changes when $x$ increases by 1, check if points represent a line based on $r$, and find $y$ when $x=20$ using the treadline equation. 2. **Formula for slope and interpretation:** The treadline equation is $$y = -5.2x + 93.4$$ where the slope is $-5.2$. The slope tells us the change in $y$ for a one unit increase in $x$. 3. **Change in $y$ when $x$ increases by 1:** Since slope $m = -5.2$, the change in $y$ is $$\Delta y = m \times \Delta x = -5.2 \times 1 = -5.2$$ 4. **Interpretation of $r$:** The correlation coefficient $r = -0.9981$ is very close to $-1$, indicating a very strong negative linear relationship. This means the points lie almost perfectly on a line with negative slope. 5. **Calculate $y$ when $x=20$ using the treadline:** Substitute $x=20$ into the equation: $$y = -5.2(20) + 93.4 = -104 + 93.4 = -10.6$$ **Final answers:** - $y$ decreases by $5.2$ when $x$ increases by $1$. - The points represent a very strong negative linear relationship (almost a perfect line). - When $x=20$, $y = -10.6$.