Find the equation of a line wiith slope -1 and cutting off an intercept of 4 units on negative direction of
(a) x-axis
(b) y-axis

Answer

To find the equation of a line with a slope of -1 and cutting off an intercept of 4 units on the negative direction of the axes, we will solve the problem in two parts: (a) for the x-axis and (b) for the y-axis.

### Part (a): Cutting off an intercept of 4 units on the negative direction of the x-axis

1. **Identify the x-intercept**: Since the line cuts off an intercept of 4 units on the negative direction of the x-axis, the x-intercept is -4. This means the line crosses the x-axis at the point (-4, 0).

2. **Use the slope-intercept form**: The slope-intercept form of a line is given by:
\[ y = mx + c \]
where \(m\) is the slope and \(c\) is the y-intercept.

3. **Substitute the slope and intercept**: We know the slope \(m = -1\) and we need to find the y-intercept \(c\). To find \(c\), we can use the x-intercept point (-4, 0):
\[ 0 = -1(-4) + c \]
\[ 0 = 4 + c \]
\[ c = -4 \]

4. **Write the equation**: Now we can write the equation of the line:
\[ y = -1x - 4 \]
or simply,
\[ y = -x - 4 \]

### Part (b): Cutting off an intercept of 4 units on the negative direction of the y-axis

1. **Identify the y-intercept**: Since the line cuts off an intercept of 4 units on the negative direction of the y-axis, the y-intercept is -4. This means the line crosses the y-axis at the point (0, -4).

2. **Use the slope-intercept form**: Again, we use the slope-intercept form:
\[ y = mx + c \]

3. **Substitute the slope and intercept**: We know the slope \(m = -1\) and the y-intercept \(c = -4\):
\[ y = -1x - 4 \]
or simply,
\[ y = -x - 4 \]

### Summary of Results
- (a) The equation of the line with slope -1 and x-intercept -4 is:
\[ y = -x - 4 \]
- (b) The equation of the line with slope -1 and y-intercept -4 is:
\[ y = -x - 4 \]