1. **Problem Statement:** Find the value of $x$ when $y = -15.5$ for the line of best fit from the first data set: | x | -2 | -1 | 0 | 1 | 2 | 3 | | y | 4 | 3 | 1 | -2| -3| -2| 2. **Find the gradient ($m$) and y-intercept ($c$):** The gradient formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Choose points $(0,1)$ and $(1,-2)$: $$m = \frac{-2 - 1}{1 - 0} = \frac{-3}{1} = -3$$ 3. **Find the y-intercept ($c$):** Use the point $(0,1)$: $$y = mx + c \Rightarrow 1 = -3 \times 0 + c \Rightarrow c = 1$$ 4. **Equation of the line:** $$y = -3x + 1$$ 5. **Find $x$ when $y = -15.5$:** Substitute $y = -15.5$: $$-15.5 = -3x + 1$$ Rearranged: $$-3x = -15.5 - 1 = -16.5$$ $$x = \frac{-16.5}{-3} = 5.5$$ **Final answer:** $$x = 5.5$$