Find the equation of the straight line through two points :
`(i) (0,2)` and `(0,4)` `(ii) (2,6)` and `(2,5)`

Answer

To find the equations of the straight lines through the given points, we will use the two-point form of the equation of a straight line. The formula is:

\[ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} \]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the two points through which the line passes.

### Part (i): Points (0, 2) and (0, 4)

1. **Identify the points**:
- Let \((x_1, y_1) = (0, 2)\)
- Let \((x_2, y_2) = (0, 4)\)

2. **Substitute the points into the formula**:
\[ \frac{y - 2}{4 - 2} = \frac{x - 0}{0 - 0} \]

3. **Simplify the equation**:
- The denominator \(0 - 0\) indicates that the line is vertical.
- Since both points have the same x-coordinate (0), the equation of the line is:
\[ x = 0 \]

### Part (ii): Points (2, 6) and (2, 5)

1. **Identify the points**:
- Let \((x_1, y_1) = (2, 6)\)
- Let \((x_2, y_2) = (2, 5)\)

2. **Substitute the points into the formula**:
\[ \frac{y - 6}{5 - 6} = \frac{x - 2}{2 - 2} \]

3. **Simplify the equation**:
- The denominator \(2 - 2\) indicates that the line is vertical.
- Since both points have the same x-coordinate (2), the equation of the line is:
\[ x = 2 \]

### Final Answers:
1. For points (0, 2) and (0, 4): **x = 0**
2. For points (2, 6) and (2, 5): **x = 2**