Answer:

Let's denote the total fare as \( y \) and the distance covered as \( x \).

The given information can be represented by the following linear equation:

\[ y = 20 + 10(x-1) \]

Here's the breakdown of the equation:

- The initial fare for the first kilometer is \( 20 \) rupees.

- For the subsequent distance (\( x - 1 \) kilometers, as the first kilometer is already considered in the initial fare), the fare is \( 10 \) rupees per kilometer.

Now, let's plot this equation on a graph to visualize it.

```python

import matplotlib.pyplot as plt

import numpy as np

# Define the linear equation

def taxi_fare(x):

   return 20 + 10 * (x - 1)

# Generate x values

x_values = np.arange(1, 15, 1)

# Calculate corresponding y values

y_values = taxi_fare(x_values)

# Plot the graph

plt.plot(x_values, y_values, label='Taxi Fare')

plt.scatter([10, 12], [taxi_fare(10), taxi_fare(12)], color='red')  # Mark points for 10km and 12km

# Labeling the axes

plt.xlabel('Distance (km)')

plt.ylabel('Fare (rupees)')

# Title of the graph

plt.title('Taxi Fare Calculation')

# Show grid

plt.grid(True)

# Show the graph

plt.legend()

plt.show()

```

In this graph:

- The x-axis represents the distance in kilometers.

- The y-axis represents the total fare in rupees.

The red points on the graph correspond to the fare for 10km and 12km, respectively. You can read the fare values from the y-axis for these points.