find the equation of line having slope 5 and length of `(3)/(2)` on y Axis.

Answer

To find the equation of a line with a given slope and y-intercept, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Slope and Y-Intercept**:
- The slope (m) is given as 5.
- The y-intercept (c) is given as \( \frac{3}{2} \).

2. **Use the Slope-Intercept Form**:
- The equation of a line in slope-intercept form is given by:
\[ y = mx + c \]
- Here, \( m \) is the slope and \( c \) is the y-intercept.

3. **Substitute the Values**:
- Substitute \( m = 5 \) and \( c = \frac{3}{2} \) into the equation:
\[ y = 5x + \frac{3}{2} \]

4. **Convert to Standard Form**:
- To convert the equation to standard form \( Ax + By + C = 0 \), we can rearrange the equation:
\[ y - 5x - \frac{3}{2} = 0 \]
- To eliminate the fraction, multiply through by 2:
\[ 2y - 10x - 3 = 0 \]
- Rearranging gives us:
\[ 10x - 2y - 3 = 0 \]

5. **Final Equation**:
- The final equation of the line is:
\[ 10x - 2y - 3 = 0 \]