Solve Linear Equation 547F12

1. **State the problem:** Solve the equation $$y + 2 = \frac{1}{6}(x - 4)$$ for $$y$$. 2. **Formula and rules:** To isolate $$y$$, subtract 2 from both sides of the equation. 3. **Intermediate work:** $$y + 2 = \frac{1}{6}(x - 4)$$ Subtract 2 from both sides: $$y + 2 - 2 = \frac{1}{6}(x - 4) - 2$$ Simplify: $$y = \frac{1}{6}(x - 4) - 2$$ 4. **Final expression:** $$y = \frac{1}{6}x - \frac{4}{6} - 2$$ Simplify the constants: $$y = \frac{1}{6}x - \frac{2}{3} - 2$$ Convert 2 to fraction with denominator 3: $$2 = \frac{6}{3}$$ So, $$y = \frac{1}{6}x - \frac{2}{3} - \frac{6}{3} = \frac{1}{6}x - \frac{8}{3}$$ 5. **Explanation:** We isolated $$y$$ by subtracting 2 from both sides and then simplified the constants to get the equation in slope-intercept form. **Final answer:** $$y = \frac{1}{6}x - \frac{8}{3}$$