Parallel Lines 0B1Bc6

1. **State the problem:** We need to find which lines among the four given are parallel. 2. **Recall the rule:** Lines are parallel if and only if their slopes are equal. 3. **Find the slope of each line:** - Line 1 is already in slope-intercept form $y = mx + b$ with slope $m = -5$. - Line 2: Given $x + \frac{1}{2} y = -4$. Solve for $y$: $$\frac{1}{2} y = -4 - x$$ $$y = 2(-4 - x) = -2x - 8$$ So slope $m = -2$. - Line 3 is given as $y = -2x + 4$, slope $m = -2$. - Line 4: Given $y + 8 = -\frac{1}{5} (x - 9)$. Expand right side: $$y + 8 = -\frac{1}{5} x + \frac{9}{5}$$ Subtract 8: $$y = -\frac{1}{5} x + \frac{9}{5} - 8 = -\frac{1}{5} x - \frac{31}{5}$$ So slope $m = -\frac{1}{5}$. 4. **Compare slopes:** - Line 1 slope: $-5$ - Line 2 slope: $-2$ - Line 3 slope: $-2$ - Line 4 slope: $-\frac{1}{5}$ Lines 2 and 3 have the same slope $-2$, so they are parallel. 5. **Final answer:** Lines 2 and 3 are parallel.