1. **State the problem:** Rearrange each linear equation into the form $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept. 2. **Formula and rules:** The slope-intercept form is $$y = mx + c$$ where $m$ is the coefficient of $x$ and $c$ is the constant. 3. **Rearranging each equation:** - For $x + y = 4$: $$y = 4 - x$$ $$y = -1x + 4$$ So, $m = -1$, $c = 4$. - For $x + 2y = 2$: $$2y = 2 - x$$ $$y = \frac{2 - x}{2}$$ $$y = \frac{2}{2} - \frac{x}{2}$$ $$y = 1 - \frac{1}{2}x$$ $$y = -\frac{1}{2}x + 1$$ - For $2x - 3y = 6$: $$-3y = 6 - 2x$$ $$3y = 2x - 6$$ (multiply both sides by $-1$) $$y = \frac{2x - 6}{3}$$ $$y = \frac{2}{3}x - 2$$ - For $x + 2y = 1$: $$2y = 1 - x$$ $$y = \frac{1 - x}{2}$$ $$y = \frac{1}{2} - \frac{x}{2}$$ $$y = -\frac{1}{2}x + \frac{1}{2}$$ 4. **Summary:** - $y = -1x + 4$ - $y = -\frac{1}{2}x + 1$ - $y = \frac{2}{3}x - 2$ - $y = -\frac{1}{2}x + \frac{1}{2}$ These are the rearranged forms of the given equations in slope-intercept form. 5. **Graphing:** Each line can be graphed by plotting the y-intercept $c$ on the y-axis and using the slope $m$ to find another point. For example, for $y = -1x + 4$, start at $(0,4)$ and go down 1 unit and right 1 unit to plot the next point. **Final answer:** The rearranged equations are: $$y = -x + 4$$ $$y = -\frac{1}{2}x + 1$$ $$y = \frac{2}{3}x - 2$$ $$y = -\frac{1}{2}x + \frac{1}{2}$$