Question

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 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

Hint: To solve this question, we will use the concept of solution of linear equation in two variables. While solving this question, we have to remember that the reason that a, degree one, polynomial equation $ax + by + c = 0$ is called a linear equation is that its geometrical representation is a straight line.

Complete step-by-step answer:
Given that,
The fare for the first kilometre is Rs. 8 and after that, the fare is Rs. 5 per km.
According to the question,
Total distance covered = x km = 1 + (x-1) km.
Total fare = Rs. y.
The fare of first kilometre = Rs. 8.
The subsequent fare = Rs. 5 per km.
So, we can write these statements in the form of equation as:
$
   \Rightarrow 8\left( 1 \right) + 5\left( {x - 1} \right) = y \\
   \Rightarrow 8 + 5x - 5 = y \\
   \Rightarrow 5x - y + 3 = 0 \\
$
This is the required linear equation of two variables.
We can also write this as:
\[ \Rightarrow y = 5x + 3\] ……….. (i)
Now, we have to draw the graph for this linear equation.
So, we have to find out the points that will satisfy the given equation.
When x = 0,
y = 5(0) + 3 = 3.
When x = 1,
y = 5(1) + 3
y = 8.
When x = 2,
y = 5(2) + 3
y = 13.
And so on.
Thus, the points that satisfy equation (i) are ( 0,3 ), ( 1,8 ), ( 2,13 ) and so on.
Now, we will plot these points on the graph.
Hence, this is the answer.

Note:Whenever we ask such types of questions, first we have to find out all the given details and then by using those details, we will make a linear equation. That will be the required linear equation. After that, we have to find out the points that will satisfy that linear equation and then by plotting those points on the graph, we will get the required answer.