# The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per $ \mathrm{km} $. Taking the distance covered as $ x \mathrm{~km} $ and total fare as Rs $ y $, write a linear equation for this information, and draw its graph.

Given:

The taxi fare in a city is $\ Rs. 8$ for the first kilometre and for the subsequent distance it is $Rs.5\ per\ kilometre$.

To do:

We have to write the linear equation by taking the distance covered as \( x \mathrm{~km} \) and total fare as \( ₹ y \) and draw its graph

Solution:

Let the total distance covered be $x\ km$.

Fare for the first kilometre $=1\times 8=Rs.\ 8$

Fare for the subsequent distance$=Rs.\ ( x-1)\times5$

According to the question,

$8+( x-1)5=y$

$\Rightarrow 8+5x-5=y$

$\Rightarrow 5x-y+3=0$

The linear equation representing the given information is $5x-y+3=0$.

We know that,

To draw a graph of a linear equation in two variables, we need at least two solutions to the given equation.

To find the solutions to the given equation $5x-y+3=0$.

This implies,

$5x-y=-3$

Let us substitute $x=0$ and $y=0$ in equation $5x-y=-3$

For $x=0$

We get,

$5(0)-y=-3$

$0-y=-3$

$y=3$

For $y=0$

We get,

$5x-0=-3$

$5x=-3$

$x=\frac{-3}{5}$

Therefore,

$(0, 3)$ and $(\frac{-3}{5}, 0)$ are two solutions of the equation$5x-y=-3$.

Hence,

The graph of the linear equation $5x-y=-3$ in two variables is,

Related Articles

- The taxi fare in a city is as follows: For the first kilometre, the fare is \( \mathrm{F} 8 \) and for the subsequent distance it is Rs. 5 per \( \mathrm{km} \). Taking the distance covered as \( x \mathrm{~km} \) and total fare as \( Rs. y \), write a linear equation for this information, and draw its graph.
- The Taxi Fare In a City is as follows : for the first kilometer the fare Is â‚¹8 and for the Subsequent distance it is â‚¹5 Per Kilometer . Taking the distance covered as X Kilometer and total fare as â‚¹y , write a Linear equation for This Information, And draw it's graph.
- The taxi fare after each \( \mathrm{km} \), when the fare is Rs 15 for the first \( \mathrm{km} \) and Rs 8 for each additional \( \mathrm{km} \), does not form an AP as the total fare (in Rs) after each \( \mathrm{km} \) is\( 15,8,8,8, \ldots \)Is the statement true? Give reasons.
- A three-wheeler scooter charges Rs. 15 for first kilometer and Rs. 8 each for every subsequent kilometer. For a distance of $x\ km$, an amount of Rs. $y$ is paid. Write the linear equation representing the above information.
- Taxi service charge Rs. 8 for kilometre and levies a fixed charge of Rs. 50. Write an algebraic expression for the above situation if the taxi is hired from x kilometre.
- In which of the following situations, does the list of numbers involved make an arithmetic progression and why?(i) The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.(ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.(iii) The cost of digging a well after every metre of digging, when it costs Rs. 150 for the first metre and rises by Rs. 50 for each subsequent metre.(iv) The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at 8% per annum.
- The car hire charges in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs. 89 and for a journey of 20 km, the charge paid is Rs. 145. What will a person have to pay for travelling a distance of 30 km?
- A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
- The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10\ km$, the charge paid is $â‚¹\ 105$ and for a journey of $15\ km$, the charge paid is $â‚¹\ 155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25\ km$.
- Thomas covers a total distance of 1056 km from city A to city C through city B. If the distance from city A to city B is 543.7 km, find the distance between city B and city C.Express the answer as a decimal.
- A lending library has a fixed charges for the first three days and an additional charge for each day thereafter. Aarushi paid Rs. 27 for a book kept for seven days. If fixed charges are Rs. x and per day charges are Rs. y. Write the linear equation representing the above information.
- For going to a city \( \mathrm{B} \) from city \( \mathrm{A} \), there is a route via city \( \mathrm{C} \) such that \( \mathrm{AC} \perp \mathrm{CB} \), \( \mathrm{AC}=2 x \mathrm{~km} \) and \( \mathrm{CB}=2(x+7) \mathrm{km} \). It is proposed to construct a \( 26 \mathrm{~km} \) highway which directly connects the two cities \( \mathrm{A} \) and \( \mathrm{B} \). Find how much distance will be saved in reaching city B from city A after the construction of the highway.
- A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530 . Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810 . Find the full first class fare from station \( \mathrm{A} \) to \( \mathrm{B} \), and also the reservation charges for a ticket.
- A taxi charges â‚¹ 9/ km and fixed charges of â‚¹ 50. If the taxi is hired for $x$ Km. Write an algebraic expression for the situation.
- The distance between the school and a student's house is \( 1 \mathrm{~km} 875 \mathrm{~m} \). Everyday she walks both ways. Find the total distance covered by her in six days.

##### Kickstart Your Career

Get certified by completing the course

Get Started