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

Transcript text: Analitik duzlemde, $d_{1}: 2 x+(m+1) y-4=0$ dogrusuile $d_{2}:-x+2 m y+1=0$ dogrvusu parales ise m deforin kaçtır?

Solution

Solution Steps

Step 1: Identify the Condition for Parallel Lines

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: \[ -\frac{-1}{2m} = \frac{1}{2m} \]

Step 2: Set the Slopes Equal

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

Step 3: Solve for $m$

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

The value of $m$ that makes the lines parallel is: \[ \boxed{m = -\frac{1}{5}} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!