Question

A taxi charges Rs 20 for the first km and Rs 12 per km for subsequent distance covered. Taking the distance covered as x km and total fare as Rs y, write a linear equation, depicting the relation in x and y.
Draw the graph between x and y.
From the graph, find the taxi charges for covering 16 km.

Answer 1

Taxi charges for the first km = Rs 20
Taxi charges for the subsequent distance covered = Rs 12 per km
Distance covered = x km (given)
Total fare = Rs y (given)
Fare charged for the distance covered leaving the first kilometre = Rs 12(x - 1)
​So, taxi charge = 20 + 12(x - 1)
But total fare = Rs y (given)
∴ y = 20 + 12x - 12 = 12x + 8
Hence, the required relation between x and y is y = 12x + 8
For, $x=0$ $\Rightarrow y=8$
For, $x=3$ $\Rightarrow y=44$
Plot these points $A(0,8),B(3,44)$ on the graph paper.
Join them and extend in both the directions.
Then, $x=16$ gives $y=200$.
So, for 16 km taxi charge = Rs 200.