An equation of the form ax+b=0 hwere a,b are real numbers and a `ne` 0 in the variable x geometrically represents ________

Answer

To solve the question, we need to analyze the equation of the form \( ax + b = 0 \) where \( a \) and \( b \) are real numbers and \( a \neq 0 \).

### Step-by-Step Solution:

1. **Start with the given equation**:
\[ ax + b = 0 \]

2. **Isolate \( x \)**:
- To find the value of \( x \), we can rearrange the equation. First, subtract \( b \) from both sides:
\[ ax = -b \]
- Next, divide both sides by \( a \) (since \( a \neq 0 \)):
\[ x = -\frac{b}{a} \]

3. **Interpret the result**:
- The equation \( x = -\frac{b}{a} \) indicates that \( x \) takes a specific value, which is a real number. This means that the solution to the equation is a single point on the x-axis.

4. **Geometric representation**:
- In a Cartesian coordinate system, this equation represents a vertical line where \( x \) is constant at the value \( -\frac{b}{a} \). This line is parallel to the y-axis.

5. **Conclusion**:
- Therefore, geometrically, the equation \( ax + b = 0 \) represents a vertical line at the point \( x = -\frac{b}{a} \).

### Final Answer:
The equation \( ax + b = 0 \) geometrically represents a vertical line at the point \( x = -\frac{b}{a} \).

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