General Form F06277

1. **State the problem:** Rewrite the equation $y= -\frac{1}{6}x-\frac{7}{6}$ into the general form $Ax + By + C = 0$. 2. **Recall the general form:** The general form of a linear equation is $$Ax + By + C = 0$$ where $A$, $B$, and $C$ are integers and $A \geq 0$. 3. **Start with the given equation:** $$y = -\frac{1}{6}x - \frac{7}{6}$$ 4. **Multiply both sides by 6 to clear denominators:** $$6y = 6 \left(-\frac{1}{6}x - \frac{7}{6}\right)$$ $$6y = \cancel{6} \times -\frac{1}{\cancel{6}} x + \cancel{6} \times -\frac{7}{\cancel{6}}$$ $$6y = -1x - 7$$ 5. **Rewrite the equation:** $$6y = -x - 7$$ 6. **Bring all terms to one side to get zero on the right:** $$x + 6y + 7 = 0$$ 7. **Final answer:** The general form is $$x + 6y + 7 = 0$$.