Question

A three-wheeler scooter charges Rs. 15 for first kilometer and Rs.8 each for every subsequent kilometer.
For a distance of 'X' kilometres, an amount of Rs. 'y' is paid.
Represent this situation algebraically as well as graphically.​

Answer 1

$\large \underline{ \underline \text{Question:}}$

A three-wheeler scooter charges Rs. 15 for first kilometer and Rs.8 each for every subsequent kilometer.

• For a distance of 'X' kilometres, an amount of Rs. 'Y' is paid.
• Represent this situation algebraically as well as graphically.

$\large \underline{ \underline \text{Solution:}}$

Assuming,

• The distance = x

• The cost for x distance = y

We know,

• Rate(Distance) = Total cost

Let substitute assumed values,

• ➺ Rate × (xkm) = ₹y

We can say that,

• ➺ Rate × [(xkm - 1km) + 1km] = ₹y
• ➺ Rate (xkm - 1km) + Rate (1km) = ₹y

As given,

• Charge for 1km = ₹15/km
• Charge for remaining distance = ₹8/km

We have,

• ➺ ₹8/km (xkm - 1km) + ₹15/km (1km) = ₹y
• ➺ ₹8x - ₹8 + ₹15 = ₹y
• ➺ ₹8x - ₹y = ₹8 - ₹15
• ➺ ₹(8x - y) = ₹(-7)

We get,

• 8x - y = -7

8x - y = -7

If x = 0,

• ➺ 8x - y = -7
• ➺ 8(0) - y = -7
• ➺ 0 - y = -7
• ➺ y = 7

Then,

• y = 7

First coordinate = (0,7)

If y = 0

• ➺ 8x - y = -7
• ➺ 8x - 0 = -7
• ➺ x = -7/8

Then,

• x = -7/8

Second coordinate = (-7/8,0)