The auto fare in a city is as follows -

For the first 4 km the fare is rs30 and for the subsequent distance it is rs5 per km. Taking the distance covered as x km and total fare as rs y. write a linear equation for this information and draw the graph.

Given: the total distance covered = x km

The total fare = Rs y

 

Fare for first 4 km = Rs 30

Fare for distance greater than 4 km = 5 Rs/ km

 

Now remaining distance = (x – 4) km

∴ fare for remaining distance = 5 (x – 4) Rs 

 

Total fare = Fare for first 4 km + fare for remaining distance 

y = 30 + 5(x – 4)

y = 30 + 5x – 20

y = 5x + 10

 

⇒ 5x – y = – 10

x– 201
y01015

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Total distance = x

Total fare = y

Fare for first km = Rs30

Remaining distance = (x-1)km

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

A.T.Q

y = 30 + 5(x-1)

y = 30 + 5x - 5

y = 25 + 5x

When x = 0,

y = 25+5(0)

y = 25

When x = 1,

y = 25+5(1)

y = 30

When x = 2,

y = 25 + 5(2)

y = 25 + 10

y = 35

Now you can easily draw the  graph.

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