Question

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 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.​

please solve this to

Answer 1

Step-by-step explanation:

given, total distance covered =x

km=1 + (x-1)km

Fare for first kilometre =£8

Fare for subsequent distance=£5 per km

Fare for next (x-1)km =5(x-1)

A.T.Q

Total fare =y

8+5(x-1)=y

8+5x-5=y

5x-y+3=0

Which is the required linear equation.

It can also be written a y=5x+3

When x=0, then Y=3, When x=1, then Y=5+3=8

When x=2, then Y=10+3=13

[Table & graph are on the attachment]

Now plot the points A(0,3), B(1,8), C(2,13) on the graph paper and join them to form a line BC, which represents the required graph of linear equation.

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)