Find the slope of the line which is perpendicular to the line `7x+11y-2=0`.

Answer

To find the slope of the line that is perpendicular to the line given by the equation \(7x + 11y - 2 = 0\), we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation of the line:
\[ 7x + 11y - 2 = 0 \]
We want to express this in the form \(y = mx + b\), where \(m\) is the slope.

### Step 2: Isolate \(y\)
To isolate \(y\), we can rearrange the equation:
\[ 11y = -7x + 2 \]

### Step 3: Divide by 11
Next, we divide every term by 11 to solve for \(y\):
\[ y = -\frac{7}{11}x + \frac{2}{11} \]

### Step 4: Identify the slope of the given line
From the equation \(y = -\frac{7}{11}x + \frac{2}{11}\), we can see that the slope \(m_1\) of the given line is:
\[ m_1 = -\frac{7}{11} \]

### Step 5: Use the relationship between slopes of perpendicular lines
The slopes of two perpendicular lines are related by the equation:
\[ m_1 \cdot m_2 = -1 \]
where \(m_2\) is the slope of the line that is perpendicular to the given line.

### Step 6: Substitute \(m_1\) into the equation
Substituting \(m_1\) into the equation:
\[ -\frac{7}{11} \cdot m_2 = -1 \]

### Step 7: Solve for \(m_2\)
To find \(m_2\), we can multiply both sides by \(-1\):
\[ \frac{7}{11} \cdot m_2 = 1 \]
Now, divide both sides by \(\frac{7}{11}\):
\[ m_2 = 1 \div \frac{7}{11} = 1 \cdot \frac{11}{7} = \frac{11}{7} \]

### Final Answer
Thus, the slope of the line that is perpendicular to the given line is:
\[ m_2 = \frac{11}{7} \]

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