Question

6. The taxi fare in a city is as follows: For the first kilometer, the fare
is Rs. 10 and for the subsequent distance it is Rs.5 per km. 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

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

$\green{\huge\underline{\sf{Solution-}}}$

According to statement,

For the first kilometer, the fare is Rs. 10 and for the subsequent distance it is Rs.5 per km.

As

• Distance covered is x km

and

• Total fare is Rs. y

Now,

• Fare for first kilometer = Rs 10

• Fare for remaining x- 1 km = 5 × (x - 1) = Rs 5x - 5

Hence, Total fare

$\rm :\longmapsto\:y = 10 + 5x - 5$

$\bf\implies \:y = 5x + 5 - - - (1)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y = 5 \times 0 + 5$

$\rm :\longmapsto\:y = 0 + 5$

$\bf\implies \:y = 5$

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

$\rm :\longmapsto\:y = 5 \times ( - 1) + 5$

$\rm :\longmapsto\:y = - 5 + 5$

$\bf\implies \:y = 0$

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

$\rm :\longmapsto\:y = 5 \times 1 + 5$

$\rm :\longmapsto\:y = 5 + 5$

$\bf\implies \:y = 10$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 5 \\ \\ \sf - 1 & \sf 0 \\ \\ \sf 1 & \sf 10 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 5), (- 1 , 0) & (1 , 10)

➢ See the attachment graph.