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

Total distance covered = x km  

Total taxi fare = ₹ y

Fare for 1km = ₹ 8

Remaining distance = (x – 1) km

∴ Fare for (x – 1)km = ₹5 x(x – 1)

Total taxi fare = ₹ 8 + ₹ 5(x – 1)

According to question,

y = 8 + 5(x – 1) 

y = 8 + 5x – 5

⇒ y = 5x + 3,

which is the required linear equation representing the given information.

For x = 0,  y = 5(0) + 3 ⇒ y = 3

For x = -1,  y = 5(-1) + 3 ⇒ y = -2

For x = -2,  y = 5(-2) + 3 ⇒ y = -7

Now, plotting the points (0, 3), (-1, -2) and (-2, -7) on a graph paper and joining them, we get a straight line PQ.
 

Thus, the line PQ is the required graph of the linear equation y = 5x + 3.