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. - Mathematics

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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.

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Solution

Total distance covered = x km

Fare for 1st kilometre = Rs 8

Fare for the rest of the distance = Rs (x − 1) 5

Total fare = Rs [8 + (− 1) 5]

= 8 + 5x − 5

= 5x + 3

5x − + 3 = 0

It can be observed that point (0, 3) and (-3/5, 0) satisfies the above equation. Therefore, these are the solutions of this equation.

x 0 -3/5
y 3 0

The graph of this equation is constructed as follows.

Here, it can be seen that variable x and y are representing the distance covered and the fare paid for that distance respectively and these quantities may not be negative. Hence, only those values of x and y which are lying in the 1st quadrant will be considered.

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Chapter 4: Linear Equations in two Variables - Exercise 4.3 [Page 74]

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NCERT Mathematics Class 9
Chapter 4 Linear Equations in two Variables
Exercise 4.3 | Q 4 | Page 74

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