Point `(0, -4)` lies on the line _______.

Options

A. `x-2y=4`
B. `2x+y=4`
C. `2x-y=4`
D. `x+y=4`

Answer

To determine which line the point (0, -4) lies on, we will substitute the coordinates of the point into each of the given equations and check if they satisfy the equation.

### Step-by-Step Solution:

1. **Check the first equation: \( x - 2y = 4 \)**
Substitute \( x = 0 \) and \( y = -4 \):
\[ 0 - 2(-4) = 4 \]
Simplifying this gives:
\[ 0 + 8 = 4 \quad \text{(which is false)} \]
Therefore, the point (0, -4) does not lie on this line.

2. **Check the second equation: \( 2x + y = 4 \)**
Substitute \( x = 0 \) and \( y = -4 \):
\[ 2(0) + (-4) = 4 \]
Simplifying this gives:
\[ 0 - 4 = 4 \quad \text{(which is false)} \]
Therefore, the point (0, -4) does not lie on this line.

3. **Check the third equation: \( 2x - 5 = 4 \)**
Substitute \( x = 0 \):
\[ 2(0) - 5 = 4 \]
Simplifying this gives:
\[ 0 - 5 = 4 \quad \text{(which is false)} \]
Therefore, the point (0, -4) does not lie on this line.

4. **Check the fourth equation: \( x + y = 4 \)**
Substitute \( x = 0 \) and \( y = -4 \):
\[ 0 + (-4) = 4 \]
Simplifying this gives:
\[ 0 - 4 = 4 \quad \text{(which is false)} \]
Therefore, the point (0, -4) does not lie on this line.

### Conclusion:
None of the provided equations satisfy the point (0, -4). Therefore, the point does not lie on any of the lines given in the options.