Question

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 10 and for subsequent distance it is Rs. 7 per kilometre. Taking the distance covered as x km and total fare as Rs. Y , write a linear equation for this information and draw its graph.​

Answer 1

Answer:

Let us consider the distance covered as x

km and total fare as Rs.y

.

Taxi fare for first kilometer =Rs.8

Taxi fare for subsequent distance =Rs.5

Total distance covered =x

Total fare =y

From the given Problem, we have

Fare for (x−1)

kilometer =5(x−1)

Since the fare for the first kilometer is equal to 8 rupees.

So, the total fare y=5(x−1)+8

Multiplying the terms, we get

⇒y=5x−5+8

Simplifying the equation, we have

⇒y=5x+3

…………………………………..(1)

Therefore, y=5x+3

is the required linear equation.

Now, Substituting the value of in Equation (1)

, we get

⇒y=5×0+3

⇒y=0+3=3

So the solution is (0,3)

Substituting the value of x=1

in Equation (1)

, we get

⇒y=5×1+3

⇒y=5+3=8

.

So the solution is (1,8)

Substituting the value of x=2

in Equation (1)

, we get

⇒y=5×2+3

⇒y=10+3=13

.

So the solution is (2,13)

.

Therefore, the coordinates of a Point are (0,3)

, (1,8)

,(2,13)

.

Now we will draw the graph using these points.