Find the equation of the straight line through the given point P(-1, -5) and having its slope equal to `9/(5)`.

Answer

To find the equation of the straight line that passes through the point P(-1, -5) and has a slope of \( \frac{9}{5} \), we can use the point-slope form of the equation of a line. The point-slope form is given by:

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

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

### Step-by-Step Solution:

1. **Identify the given values**:
- Point \( P(-1, -5) \) gives us \( x_1 = -1 \) and \( y_1 = -5 \).
- Slope \( m = \frac{9}{5} \).

2. **Substitute the values into the point-slope form**:
\[ y - (-5) = \frac{9}{5}(x - (-1)) \]
This simplifies to:
\[ y + 5 = \frac{9}{5}(x + 1) \]

3. **Distribute the slope on the right side**:
\[ y + 5 = \frac{9}{5}x + \frac{9}{5} \]

4. **Isolate \( y \)** by subtracting 5 from both sides:
\[ y = \frac{9}{5}x + \frac{9}{5} - 5 \]

5. **Convert 5 into a fraction with a denominator of 5**:
\[ 5 = \frac{25}{5} \]
So, we have:
\[ y = \frac{9}{5}x + \frac{9}{5} - \frac{25}{5} \]

6. **Combine the constant terms**:
\[ y = \frac{9}{5}x - \frac{16}{5} \]

7. **To express it in standard form, multiply through by 5 to eliminate the fraction**:
\[ 5y = 9x - 16 \]

8. **Rearranging gives us the standard form**:
\[ 9x - 5y - 16 = 0 \]

### Final Equation:
The equation of the straight line is:
\[ 9x - 5y - 16 = 0 \]