Find the equation of t he straight line through the given point P and having the given slope m if
`P(-1, -5), m=(-6)/(11)`

Answer

To find the equation of the straight line that passes through the point \( P(-1, -5) \) and has a slope \( m = -\frac{6}{11} \), we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

### Step 1: Identify the values
Here, we have:
- \( (x_1, y_1) = (-1, -5) \)
- \( m = -\frac{6}{11} \)

### Step 2: Substitute the values into the point-slope formula
Substituting the values into the equation:

\[ y - (-5) = -\frac{6}{11}(x - (-1)) \]

This simplifies to:

\[ y + 5 = -\frac{6}{11}(x + 1) \]

### Step 3: Distribute the slope on the right side
Now, distribute the slope \( -\frac{6}{11} \):

\[ y + 5 = -\frac{6}{11}x - \frac{6}{11} \]

### Step 4: Rearrange the equation
Next, we want to isolate \( y \) on one side. To do this, we subtract 5 from both sides:

\[ y = -\frac{6}{11}x - \frac{6}{11} - 5 \]

### Step 5: Convert -5 to a fraction
To combine the terms, convert -5 to a fraction with a denominator of 11:

\[ -5 = -\frac{55}{11} \]

Now substitute this back into the equation:

\[ y = -\frac{6}{11}x - \frac{6}{11} - \frac{55}{11} \]

### Step 6: Combine the constant terms
Combine the constant terms on the right side:

\[ y = -\frac{6}{11}x - \frac{61}{11} \]

### Step 7: Rearranging to standard form
To express this in standard form \( Ax + By + C = 0 \), we can rearrange the equation:

\[ \frac{6}{11}x + y + \frac{61}{11} = 0 \]

Multiplying through by 11 to eliminate the fraction gives:

\[ 6x + 11y + 61 = 0 \]

### Final Equation
Thus, the equation of the straight line is:

\[ 6x + 11y + 61 = 0 \]

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