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.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

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.

JEE

NEET

Foundation JEE

Foundation NEET

CBSE