Standard To Slope 455B70

1. **State the problem:** Convert the equation $$8x + 6y = -6$$ into slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 2. **Isolate $$y$$:** Start by moving $$8x$$ to the right side by subtracting $$8x$$ from both sides: $$8x + 6y = -6$$ $$6y = -6 - 8x$$ 3. **Divide both sides by 6 to solve for $$y$$:** $$y = \frac{-6 - 8x}{6}$$ 4. **Simplify the fraction:** Split the fraction into two parts: $$y = \frac{-6}{6} - \frac{8x}{6}$$ Simplify each term: $$y = -1 - \frac{8}{6}x$$ 5. **Reduce the fraction $$\frac{8}{6}$$:** $$\frac{8}{6} = \frac{\cancel{2} \times 4}{\cancel{2} \times 3} = \frac{4}{3}$$ So, $$y = -1 - \frac{4}{3}x$$ 6. **Rewrite in slope-intercept form:** $$y = -\frac{4}{3}x - 1$$ **Final answer:** The slope-intercept form is $$y = -\frac{4}{3}x - 1$$. This means the slope $$m = -\frac{4}{3}$$ and the y-intercept $$b = -1$$.