1. The problem is to analyze and graph the given linear equations: - $y = 3x - 4$ - $y = -\frac{1}{2}x + 3$ - $2x + y = 1$ - $x - 2y = 8$ 2. We start by rewriting all equations in slope-intercept form $y = mx + b$ for easier graphing and analysis. 3. The first equation is already in slope-intercept form: $$y = 3x - 4$$ where slope $m = 3$ and y-intercept $b = -4$. 4. The second equation is also in slope-intercept form: $$y = -\frac{1}{2}x + 3$$ where slope $m = -\frac{1}{2}$ and y-intercept $b = 3$. 5. For the third equation $2x + y = 1$, solve for $y$: $$y = 1 - 2x$$ which is in slope-intercept form with slope $m = -2$ and y-intercept $b = 1$. 6. For the fourth equation $x - 2y = 8$, solve for $y$: $$x - 2y = 8$$ $$-2y = 8 - x$$ $$y = \frac{8 - x}{-2} = \frac{\cancel{8} - x}{\cancel{-2}} = -4 + \frac{x}{2}$$ More precisely: $$y = -4 + \frac{1}{2}x$$ or $$y = \frac{1}{2}x - 4$$ where slope $m = \frac{1}{2}$ and y-intercept $b = -4$. 7. Summary of all lines in slope-intercept form: - $y = 3x - 4$ - $y = -\frac{1}{2}x + 3$ - $y = -2x + 1$ - $y = \frac{1}{2}x - 4$ These forms allow us to graph each line by plotting the y-intercept and using the slope to find other points. Final answer: The four lines are $y=3x-4$, $y=-\frac{1}{2}x+3$, $y=-2x+1$, and $y=\frac{1}{2}x-4$ in slope-intercept form, ready for graphing.