Questions: Analitik düzlemde, d1: 2x + (m+1)y - 4 = 0 doğrusu ile d2: -x + 2my + 1 = 0 doğrusu paralel ise m değeri kaçtır?

Solution Steps

For two lines to be parallel, their slopes must be equal. The general form of a line is $ax + by + c = 0$, and the slope of the line is given by $-\frac{a}{b}$.

For the line $d_1: 2x + (m+1)y - 4 = 0$, the slope is: $$-\frac{2}{m+1}$$

For the line $d_2: -x + 2my + 1 = 0$, the slope is: $$-\frac{-1}{2m} = \frac{1}{2m}$$

Since the lines are parallel, set the slopes equal to each other: $$-\frac{2}{m+1} = \frac{1}{2m}$$

Cross-multiply to solve for $m$: $$-2 \cdot 2m = 1 \cdot (m+1)$$ $$-4m = m + 1$$

Add $4m$ to both sides: $$0 = 5m + 1$$

Subtract 1 from both sides: $$-1 = 5m$$

Divide by 5: $$m = -\frac{1}{5}$$

Final Answer