What is the slope of the line `2(x+2y)=0`

Options

A. `(1)/(2)`
B. `-2`
C. `-(1)/(2)`
D. `0`

Answer

To find the slope of the line given by the equation \(2(x + 2y) = 0\), we can follow these steps:

### Step 1: Expand the equation
Start by expanding the equation:
\[ 2(x + 2y) = 0 \]
Distributing the 2 gives:
\[ 2x + 4y = 0 \]

### Step 2: Rearrange the equation
Next, we want to rearrange this equation into the slope-intercept form \(y = mx + c\). To do this, isolate \(y\):
\[ 4y = -2x \]

### Step 3: Solve for \(y\)
Now, divide both sides by 4 to solve for \(y\):
\[ y = -\frac{2}{4}x \]
This simplifies to:
\[ y = -\frac{1}{2}x \]

### Step 4: Identify the slope
In the equation \(y = mx + c\), the coefficient \(m\) represents the slope. From our equation, we can see that:
\[ m = -\frac{1}{2} \]

### Conclusion
Thus, the slope of the line is:
\[ \text{slope} = -\frac{1}{2} \]

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