Graph
Line passin through (0,0) having constant term O
`ax+by+c=0" "(a!=0,b!=0,c=0)` passes through

Options

A. (0,0)
B. (0,1)
C. (1,1)
D. (10,17)

Answer

To solve the problem, we need to analyze the equation of the line given in the question and determine the points through which it passes.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation given is in the form \( ax + by + c = 0 \). We know that the constant term \( c = 0 \).
- Therefore, the equation simplifies to:
\[ ax + by = 0 \]

2. **Rearranging the Equation**:
We can rearrange this equation to express \( y \) in terms of \( x \):
\[ by = -ax \]
Dividing both sides by \( b \) (since \( b \neq 0 \)):
\[ y = -\frac{a}{b}x \]

3. **Identifying the Line**:
The equation \( y = -\frac{a}{b}x \) represents a straight line that passes through the origin (0,0). This is because when \( x = 0 \), \( y \) also equals 0.

4. **Finding Points on the Line**:
Since the line passes through the origin, we need to check which of the given options also includes the point (0,0). The options provided are:
- (0, 0)
- (0, 1)
- (1, 1)
- (1, 0)
- (1, 7)

Among these options, the point (0,0) is clearly on the line.

5. **Conclusion**:
The line represented by the equation \( ax + by = 0 \) indeed passes through the point (0,0).

### Final Answer:
The line passes through the point (0, 0).