Question

the auto rickshaw fare in a city is charged Rs 10 for the first kilometre and @ Rs 4 per km for subsequent distance coverage write the linear equation to express the above statement draw the graph of the linear equation

Answer 1

Solution :-

Let the total distance covered be x km

and, the total fare be Rs. y 

Since, Total fare = fare for the first kilometer + fare for the remaining kilometer of distance  ...........................(1)

We know that the fare for first kilometer is Rs. 10

Fare for the remaining kilometers i.e. (x - 1)

= 4(x - 1)

Put values in (1)

⇒ y = 10(1) + 4(x - 1)

⇒ y = 10 + 4x - 4

⇒ y = 4x + 6

When x = 0, we have, y = 4 × (0) + 6, So, y = 6

When x = - 1, we have, y = 4 × (- 1) + 6, = - 4 + 6

So, y = 2

 

When x = - 2, we have, y = 4 × (- 2) + 6 = - 8 + 6

So, y = - 2

x = 0 ; y = 6

x = - 1 ; y = 2

x = - 2 ; y = - 2

Now, you can draw the graph easily.

Answer 2

Answer:

let's take the fare for the first km =rs10

and

fair for subsequent km =(x-1)

and the total fair be y

so

y= 10 + 4(x-1)

=10 + 4x-4

y= 4x + 6

therefore

when

x=0

4(0)+6=6=y

x=1

4(1)+6=10=y

x=2

4(2)+6=12=y

x=-1

4(-1)+6=2=y

know you can easily plot in your graph