The equation of a straight line on a point (3, -5) and slope 2 is:

Options

A. 3x-2y-5=0
B. 3x-5y-2=0
C. 2x-y-11=0
D. 5x-2y+3=0

Answer

To find the equation of a straight line that passes through the point (3, -5) with a slope of 2, 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 \( (x_1, y_1) = (3, -5) \)
- Slope \( m = 2 \)

2. **Substitute the values into the point-slope formula:**
\[ y - (-5) = 2(x - 3) \]
This simplifies to:
\[ y + 5 = 2(x - 3) \]

3. **Distribute the slope on the right side:**
\[ y + 5 = 2x - 6 \]

4. **Rearrange the equation to isolate \( y \):**
\[ y = 2x - 6 - 5 \]
Simplifying gives:
\[ y = 2x - 11 \]

5. **Rearrange to standard form:**
To convert to the standard form \( Ax + By + C = 0 \):
\[ 2x - y - 11 = 0 \]

### Final Equation:
The equation of the line is:
\[ 2x - y - 11 = 0 \]