Question

The auto rickshaw fare in a city is charged as rs 10 for the first km and at rs 4 per km for subsequent distance covered write the linear equation to express the above statement and also draw the graph

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:

y=4x+6,

Step-by-step explanation:

Let the total distance be x km

and total cost be y

now, 10rs for 1st km, and 4Rs. per km for rest

so,

y=1(10)+4(x-1)

y=4x+6,

 

sub,

x=-2,y=-2

x=-1, y=2

 

so plot points (-2,-2),(-1,2)

scale : 1cm = 1 unit on both axis