Question

the autorickshaw fare in a city is charged rs 10 for the first kilometer and @ rs 4 per kilometer for subsequent distance covered. write the linear equation to express the above statement. draw the graph of the linear equation>

Answer 1

linear equation...

let subsequent distance =x

eq. 10+4x=y

where y is total amount

Answer 2

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The autorickshaw fare in a city is charged 10Rs for the first kilometer and 4Rs per kilometer for subsequent distance covered.

Write the linear equation to express the above-given statement.

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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)

$\implies \tt4(x - 1)$

• Put values in (1)

$\implies \tt{y = 10(1) + 4(x - 1)}$

$\implies \tt{ y = 10 + 4x - 4}$

$\implies \tt{y = 4x + 6}$

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