If the slope of a line is not defined then the line :

Options

A. is parallel to x-axis
B. is parallel to y-axis
C. passcs through the origin
D. cut x and y-axes .

Answer

To solve the question "If the slope of a line is not defined, then the line:", we need to analyze what it means for a line to have an undefined slope.

### Step-by-Step Solution:

1. **Understanding Slope**:
The slope (m) of a line is defined as the change in y (rise) over the change in x (run). Mathematically, it is represented as:
\[ m = \frac{\Delta y}{\Delta x} \]
If the slope is undefined, it means that \(\Delta x = 0\), which implies that the line is vertical.

**Hint**: Recall that the slope is a measure of how steep a line is. If the line goes straight up and down, the slope is undefined.

2. **Identifying the Line**:
A line with an undefined slope is vertical. The equation of a vertical line can be expressed in the form:
\[ x = k \]
where \(k\) is a constant. This means that for every value of y, x remains constant.

**Hint**: Think about how a vertical line behaves on a graph. It does not change in the x-direction.

3. **Conclusion**:
Therefore, if the slope of a line is not defined, the line must be vertical. This means it is parallel to the y-axis.

**Hint**: Visualize the coordinate plane and consider the orientation of lines. A vertical line runs parallel to the y-axis.

### Final Answer:
If the slope of a line is not defined, then the line is parallel to the y-axis.