1. **State the problem:** Given the table of values for $x$ and $y$, find the equation of the line that fits these points. 2. **Recall the formula for a linear function:** The general form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$ using two points:** Choose points $(-2,9)$ and $(3,-6)$. $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 9}{3 - (-2)} = \frac{-15}{5} = -3$$ 4. **Use the slope and one point to find $b$:** Using point $(-2,9)$: $$9 = -3(-2) + b$$ $$9 = 6 + b$$ $$b = 9 - 6 = 3$$ 5. **Write the equation:** $$y = -3x + 3$$ 6. **Verify with another point:** Using $(8,-21)$: $$y = -3(8) + 3 = -24 + 3 = -21$$ which matches the table. **Final answer:** $$y = -3x + 3$$