Question

The taxi fare in a city as follows: For the first Kilometer, the fare is Rs. 7 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

Step-by-step explanation:

Given :-

The taxi fare in a city as follows: For the first Kilometer, the fare is Rs. 7 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs y.

To find :-

Write a linear equation for this information and draw its graph ?

Solution :-

Writting the linear equation :-

The taxi fare of first kilometre = Rs. 7

The fare for the subsequent distance = Rs. 5 per km

So,

Total taxi fare for two kilometres

= 7+(2-1)(5)

= 7+5

= 12

The taxi fare for three kilometres

= 7+(3-1)(5)

= 7+2(5)

= 7+10

= 17

The texi fare for the x kilometres

= 7+(x-1)(5)

= 7+(5x-5)

= 7-5+5x

= 5x+2

So, The total fare for x kilometres = Rs. 5x+2

According to the given problem

The total fare for x kilometres = Rs. y

=> y = 5x+2

=>5x-y+2 = 0

This is a linear equation in two variables

Graph of the equation :-

We have y = 5x+2

The points are (0,7) ,(1,12) , (2,17), (-1,-3) , (-2,-8) ,(-3,-13)

Scale :-

On taking x - axis 1 cm. = 1 unit

On y - axis 1 cm = 2 units

Observation :-

• The graph of the given equation is a straight line joining by the points after plotting in the graph.

Result :-

• The graph is a straight line.

• The linear equation in two variables has infinitely number of many solutions.

Definition :-

A linear equation has two variables is called a linear equation in two variables.

General form :-

The general form of the linear equation in two variables is ax+by+c = 0 where a and b both are not equal to zero.