Question

$\large \purple{\bf{ Question - }}$

A taxi fare in a city is as follows :
For the first kilometre the fare is ₹8 and for the subsequent distance it is ₹5.Taking the distance covered as "x" km and total fare as ₹y.

Write a linear equation for this information and draw its graph.
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Answer 1

Answer:

x0 12 y38 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)

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

A taxi fare in a city is as follows :

• For the first kilometre, the fare is ₹ 8.

• For the subsequent distance, it is ₹ 5.

Further given that,

• Total distance covered = x km

• Total fare = ₹ y

So, according to statement,

$\sf \: y = 1 \times 8 + (x - 1) \times 5$

$\sf \: y = 8 + 5x - 5$

$\bf\implies \:\boxed{ \sf{ \:\bf \: y = 5x + 3 \: \: }}$

Substituting 'x = 1' in the given equation, we get

$\sf \: y = 5 \times 1 + 3$

$\sf \: y = 5 + 3$

$\bf\implies \:y = 8$

Substituting 'x = 2' in the given equation, we get

$\sf \: y = 5 \times 2 + 3$

$\sf \: y = 10 + 3$

$\bf\implies \:y = 13$

Substituting 'x = 3' in the given equation, we get

$\sf \: y = 5 \times 3 + 3$

$\sf \: y = 15 + 3$

$\bf\implies \:y = 18$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 8 \\ \\ \sf 2 & \sf 13 \\ \\ \sf 3 & \sf 18 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (1 , 8), (2 , 13) & (3 , 18)

➢ See the attachment graph.