1. The problem provides a set of points with coordinates $(X, Y)$: $(-3, -5), (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7), (4, 9)$. We want to find the equation of the function that relates $X$ to $Y$. 2. We suspect a linear relationship of the form $$Y = mX + b$$ where $m$ is the slope and $b$ is the $Y$-intercept. 3. To find the slope $m$, use two points, for example $(-3, -5)$ and $(-2, -3)$: $$m = \frac{Y_2 - Y_1}{X_2 - X_1} = \frac{-3 - (-5)}{-2 - (-3)} = \frac{-3 + 5}{-2 + 3} = \frac{2}{1} = 2$$ 4. Now find $b$ by substituting $m=2$ and one point, say $(0,1)$, into the equation: $$1 = 2 \times 0 + b \implies b = 1$$ 5. The equation of the line is therefore: $$Y = 2X + 1$$ 6. Verify with another point, for example $(3,7)$: $$Y = 2 \times 3 + 1 = 6 + 1 = 7$$ which matches the given $Y$ value. 7. Thus, the function relating $X$ and $Y$ is $$\boxed{Y = 2X + 1}$$.