Find the equation of the line parallel to x-axis and :
`(i)` passing through the point `(3,-4)`
`(ii)` passing through the point `(0,2)`
`(iii)` has intercept on the y-axis as `-2`.

Answer

To find the equation of a line parallel to the x-axis, we need to understand that such lines have a constant y-value. The general equation of a line parallel to the x-axis can be expressed as:

\[ y = k \]

where \( k \) is a constant representing the y-coordinate of any point on the line.

Now, let's solve the three parts of the question step by step.

### (i) Find the equation of the line passing through the point (3, -4).

1. **Identify the y-coordinate**: The point given is (3, -4). The y-coordinate is -4.
2. **Write the equation**: Since the line is parallel to the x-axis, the equation will be:
\[ y = -4 \]

### (ii) Find the equation of the line passing through the point (0, 2).

1. **Identify the y-coordinate**: The point given is (0, 2). The y-coordinate is 2.
2. **Write the equation**: The equation of the line parallel to the x-axis will be:
\[ y = 2 \]

### (iii) Find the equation of the line that has an intercept on the y-axis as -2.

1. **Identify the y-intercept**: The y-intercept is given as -2. This means the line crosses the y-axis at the point (0, -2).
2. **Write the equation**: The equation of the line parallel to the x-axis will be:
\[ y = -2 \]

### Final Answers:
1. For the line passing through (3, -4): \( y = -4 \)
2. For the line passing through (0, 2): \( y = 2 \)
3. For the line with y-intercept -2: \( y = -2 \)

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