1. **State the problem:** Find the equation of the line passing through the points $(-12, -6)$ and $(0, 6)$ in slope-intercept form $y=mx+b$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** Using the points $(-12, -6)$ and $(0, 6)$, $$m=\frac{6 - (-6)}{0 - (-12)}=\frac{6 + 6}{0 + 12}=\frac{12}{12}=1$$ 4. **Use slope-intercept form:** The equation is $y=mx+b$. We know $m=1$, so $$y=1\cdot x + b = x + b$$ 5. **Find $b$ (y-intercept):** Substitute point $(0,6)$ into the equation: $$6 = 1 \times 0 + b \Rightarrow 6 = b$$ 6. **Final equation:** $$y = x + 6$$ This is the fully simplified slope-intercept form of the line passing through the given points.