Question

The taxi fare in a city is as follows: For the first kilometre, the fares 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.

Answer 1

Total distance covered = x km

Fare for 1st kilometre = Rs 8

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

5 Total fare = Rs [8 + (x − 1) 5] y = 8 + 5x − 5

y = 5x + 3

5x − y + 3 = 0

It can be observed that point (0, 3) and 9-3/5,0) 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 1st quadrant will be considered.