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 it's graph.​

Answer 1

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$\large\bf{\underline{\underline{\purple{Answer:}}}}$

$\huge\Rightarrow{\bigstar{\boxed{\sf{\red{y=5x+3}}}}}$

$\large\bf{\underline{\underline{\orange{Explanation:}}}}$

$\displaystyle{\sf{Total\:distance\:covered\:=\:x\:km}}$

$\displaystyle{\sf{Total\:fare\:=\: ₹ y}}$

$\displaystyle{\sf{Fare\:for\:the\:first\:kilometre\:=\: ₹ 8}}$

$\displaystyle{\sf{According\:to\:the\:question,}}$

:$\Rightarrow{\sf{y=8+5(x-1)}}$

:$\Rightarrow{\sf{y=8+5x-5}}$

:$\Rightarrow{\boxed{\sf{\pink{y=5x+3}}}}$

and then we plot the points (0,3) and (1,8) on the graph paper and join the same by ruler to get the line which is the graph of equation y = 5x + 3.

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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)