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 Rs y, write a linear equation depicting the relation in x and y.
Draw the graph between x and y.
From your graph find the taxi charges for covering 16 km.
Ans. y = 12x + 8, Rs 200
Total distance covered = x km
Total fare = Rs y
Charges for 1 km = Rs 20
Charges for 2 kms = Rs 20 + Rs 12
Charges for 3 kms = Rs 20 + Rs 12 × 2
Continuing, we get,
Charges for (x – 1) kms = Rs 20 + Rs 12 × (x – 2)
Charges for x kms = Rs 20 + Rs 12 × (x – 1)
Total fare = Rs y
Therefore,
Total fare = Charges for x kms
⇒ y = 20 + 12 × (x – 1)
⇒ y = 20 + 12x – 12
⇒ y = 12x + 8
Let x = 1 then, y = 12x + 8
⇒ y = 12× 1 + 8
⇒ y = 12 + 8
⇒ y = 20
Let x = 5 then, y = 12x + 8
⇒ y = 12× 5 + 8
⇒ y = 60 + 8
⇒ y = 68
Let x = 10 then, y = 12x + 8
⇒ y = 12× 10 + 8
⇒ y = 120 + 8
⇒ y = 128
Plotting, (1, 20), (5, 68) and (10, 128) on the graph we get,
The blue line indicates the required graph of y = 12x + 8
When x = 16, we take 16 on x axis.
Draw a line from 16 on x axis which is parallel to y axis and meets the blue line.
Clearly from the graph the value at y axis is 200
Therefore, taxi charges at covering 16 km = Rs 200