Question

the taxi fare in a city is follow : for first k m the fare is ₹ 50 and for the subsequent distance it is ₹20 per km taking the distance covered as x km. total fare as ₹ y. vital linear equation for this information and draw its graph

Answer 1

Answer:

◦•●◉✿ 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✿◉●•◦

Answer 2

Answer:

Given that,

The fare for the first kilometre is Rs. 8 and after that, the fare is Rs. 5 per km.

According to the question,

Total distance covered = x km = 1 + (x-1) km.

Total fare = Rs. y.

The fare of first kilometre = Rs. 8.

The subsequent fare = Rs. 5 per km.

So, we can write these statements in the form of equation as:

⇒8(1)+5(x−1)=y⇒8+5x−5=y⇒5x−y+3=0

This is the required linear equation of two variables.

We can also write this as:

⇒y=5x+3

……….. (i)

Now, we have to draw the graph for this linear equation.

So, we have to find out the points that will satisfy the given equation.

When x = 0,

y = 5(0) + 3 = 3.

When x = 1,

y = 5(1) + 3

y = 8.

When x = 2,

y = 5(2) + 3

y = 13.

And so on.

Thus, the points that satisfy equation (i) are ( 0,3 ), ( 1,8 ), ( 2,13 ) and so on.

Now, we will plot these points on the graph.

Hence, this is the answer.

Note:Whenever we ask such types of questions, first we have to find out all the given details and then by using those details, we will make a linear equation. That will be the required linear equation. After that, we have to find out the points that will satisfy that linear equation and then by plotting those points on the graph, we will get the required answer.