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 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 (-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.
