Question

the taxi fare in a city is as follows: for the first kilometre, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹y , write a linear equation for this information, and draw its graph.​

Answer 1

SOLUTION:

Total fare of ₹ y for covering distance of x kilometres is given by,

y = 8 + 5 × ( x - 1 )

or, y = 8 + 5x - 5

or, y = 5x + 3 _______(i)

This is the required linear equation for the given information.

Putting x = 0 in (i), we get y = 3

Putting x = 1 in (i), we get y = 8

Thus, we have the following information or solutions exhibiting the coordinates of two points on the line y = 5x + 3.

Solutions : (0, 3) & (1, 8).

Plotting points (0, 3) and (1, 8) on the graph paper in drawing a line passing through them, we obtain the graph of the line represented by the linear equation (i) as shown in the attachment.

Answer 2

:

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-- :

x 0  1 2

y 3 8  13

Taxi fare for first kilometer = Rs. 8

Taxi fare for subsequent distance = Rs. 5

Total distance covered =x

Total fare =y

Since the fare for first kilometer = Rs.8

According to problem,

Fare for (x–1) kilometer = 5(x−1)

So, the total fare y=5(x−1)+8

⇒y=5(x−1)+8

⇒y=5x–5+8

⇒y=5x+3

Hence, y=5x+3 is the required linear equation.

Now the equation is

y=5x+3    ...(1)

Now, putting the value x=0 in (1)

y=5×0+3

y=0+3=3 So the solution is (0,3)

Putting the value x=1 in (1)

y=5×1+3

y=5+3=8. So the solution is (1,8)

Putting the value x=2 in (1)

y=5×2+3

y=10+3=13. So the solution is (2,13)