The taxi fare in a city is as follows:- For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

#### Solution

Total distance covered = *x* km

Fare for 1^{st} kilometre = Rs 8

Fare for the rest of the distance = Rs (*x* − 1) 5

Total fare = Rs [8 + (*x *− 1) 5]

*y *= 8 + 5*x* − 5

*y *= 5*x* + 3

5*x* − *y *+ 3 = 0

It can be observed that point (0, 3) and (-3/5, 0) satisfies the above equation. Therefore, these are the solutions of this equation.

x | 0 | -3/5 |

y | 3 | 0 |

The graph of this equation is constructed as follows.

Here, it can be seen that variable *x* and *y* are representing the distance covered and the fare paid for that distance respectively and these quantities may not be negative. Hence, only those values of *x* and *y* which are lying in the 1^{st} quadrant will be considered.