1. **State the problem:** Given the table of values for $X$ and $Y$, find the equation of the line that fits these points. 2. **Formula used:** The points suggest a linear relationship of the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Use the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(0, -3)$ and $(1, 2)$: $$m = \frac{2 - (-3)}{1 - 0} = \frac{5}{1} = 5$$ 4. **Find the y-intercept $b$:** Substitute $m=5$ and point $(0, -3)$ into $y = mx + b$: $$-3 = 5 \times 0 + b \implies b = -3$$ 5. **Write the equation:** $$y = 5x - 3$$ 6. **Verify with other points:** For $x=2$, $y = 5(2) - 3 = 10 - 3 = 7$ (matches table) For $x=3$, $y = 5(3) - 3 = 15 - 3 = 12$ (matches table) **Final answer:** $$y = 5x - 3$$