Question

The taxi fare in a city is as follows; for the first km, the fare is Rs, 25 and for the subsequent distance it is Rs. 14 per km . Taking the distance covered as x km and total fare as Rs.y, write a linear equation for this information and draw its graph (3 marks )

Answer 1

25+14(x-1)=y

y=25+14x-14

y=14x+11

Therefore slope is 14 and y intercept is 11

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Answer 2

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x 0  1 2

y 3 8  13

Taxi fare for first kilometer = Rs. 8

Taxi fare for subsequent distance = Rs. 5

Total distance covered =x

Total fare =y

Since the fare for first kilometer = Rs.8

According to problem,

Fare for (x–1) kilometer = 5(x−1)

So, the total fare y=5(x−1)+8

⇒y=5(x−1)+8

⇒y=5x–5+8

⇒y=5x+3

Hence, y=5x+3 is the required linear equation.

Now the equation is

y=5x+3    ...(1)

Now, putting the value x=0 in (1)

y=5×0+3

y=0+3=3 So the solution is (0,3)

Putting the value x=1 in (1)

y=5×1+3

y=5+3=8. So the solution is (1,8)

Putting the value x=2 in (1)

y=5×2+3

y=10+3=13. So the solution is (2,13)