The spring force is given by `F=-kx`, here k is a constant and x is the deformation of spring. The `F-x` graph is

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Explanation

To analyze the spring force given by the equation \( F = -kx \), we will derive the characteristics of the \( F \) versus \( x \) graph step by step.

### Step 1: Understand the Equation
The equation \( F = -kx \) indicates that the force \( F \) exerted by the spring is directly proportional to the displacement \( x \) from its equilibrium position, with \( k \) being the spring constant. The negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement.

### Step 2: Identify the Variables
In this equation:
- \( F \) is the force exerted by the spring.
- \( x \) is the displacement or deformation of the spring from its equilibrium position.
- \( k \) is a positive constant known as the spring constant.

### Step 3: Determine the Type of Graph
The equation \( F = -kx \) can be compared to the linear equation \( y = mx \), where:
- \( y \) corresponds to \( F \),
- \( x \) corresponds to \( x \),
- \( m \) (the slope) corresponds to \(-k\).

### Step 4: Analyze the Slope
Since \( k \) is a positive constant, the slope of the graph \( F \) versus \( x \) is negative (\(-k\)). This means that as \( x \) increases, \( F \) decreases, indicating a linear relationship with a negative slope.

### Step 5: Identify the Intercept
The equation \( F = -kx \) passes through the origin (0,0) because when \( x = 0 \), \( F \) also equals 0. Therefore, the graph intercepts the origin.

### Step 6: Sketch the Graph
The graph of \( F \) versus \( x \) will be a straight line that:
- Starts at the origin (0,0),
- Has a negative slope,
- Extends downward as \( x \) increases.

### Conclusion
The \( F-x \) graph is a straight line passing through the origin with a negative slope.