1. **State the problem:** Find the slope and y-intercept of the line given by the equation $6x + 2y = 5$. 2. **Rewrite the equation in slope-intercept form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.** Start with: $$6x + 2y = 5$$ Subtract $6x$ from both sides: $$\cancel{6x} + 2y - \cancel{6x} = 5 - 6x$$ $$2y = -6x + 5$$ Divide both sides by 2: $$\frac{2y}{\cancel{2}} = \frac{-6x + 5}{\cancel{2}}$$ $$y = -3x + \frac{5}{2}$$ 3. **Identify slope and y-intercept:** Slope $m = -3$ Y-intercept $b = \frac{5}{2}$ --- 4. **State the problem:** Find the slope and y-intercept of the line given by the equation $4x - 3y = -6$. 5. **Rewrite the equation in slope-intercept form:** Start with: $$4x - 3y = -6$$ Subtract $4x$ from both sides: $$\cancel{4x} - 3y - \cancel{4x} = -6 - 4x$$ $$-3y = -4x - 6$$ Divide both sides by $-3$: $$\frac{-3y}{\cancel{-3}} = \frac{-4x - 6}{\cancel{-3}}$$ $$y = \frac{-4x}{-3} + \frac{-6}{-3} = \frac{4}{3}x + 2$$ 6. **Identify slope and y-intercept:** Slope $m = \frac{4}{3}$ Y-intercept $b = 2$ --- 7. **State the problem:** Find the slope and y-intercept of the line given by the equation $3y + 2x = 3y - 14$. 8. **Simplify the equation:** Subtract $3y$ from both sides: $$3y + 2x - 3y = 3y - 14 - 3y$$ $$2x = -14$$ 9. **Rewrite in slope-intercept form:** Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{-14}{\cancel{2}}$$ $$x = -7$$ This is a vertical line where $x = -7$. 10. **Identify slope and y-intercept:** A vertical line has an undefined slope. It does not have a y-intercept because it never crosses the y-axis. --- **Final answers:** 22) Slope: $-3$, y-Intercept: $\frac{5}{2}$ 23) Slope: $\frac{4}{3}$, y-Intercept: $2$ 24) Slope: undefined, y-Intercept: none (vertical line)