Slope of a line which cuts off intercepts of equal lengths on the axes is

Options

A. `-1`
B. `0`
C. `2`
D. `sqrt(3)`

Explanation

To find the slope of a line that cuts off intercepts of equal lengths on the axes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Intercepts**:
Let the x-intercept and y-intercept of the line be equal. We denote this common length as 'a'. Therefore, the x-intercept is 'a' and the y-intercept is also 'a'.

2. **Equation of the Line in Intercept Form**:
The intercept form of a line is given by:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]
Since both intercepts are equal (i.e., \( a = b \)), we can substitute \( b \) with \( a \):
\[ \frac{x}{a} + \frac{y}{a} = 1 \]

3. **Simplifying the Equation**:
Multiplying through by 'a' to eliminate the denominators gives:
\[ x + y = a \]

4. **Rearranging to Slope-Intercept Form**:
We can rearrange this equation to express 'y' in terms of 'x':
\[ y = -x + a \]

5. **Identifying the Slope**:
In the slope-intercept form \( y = mx + c \), the coefficient of 'x' represents the slope (m). From our equation:
\[ m = -1 \]

### Final Answer:
The slope of the line which cuts off intercepts of equal lengths on the axes is \( -1 \).

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