Question

The taxi fare in a city is as follows: for the first kilometer , 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 Rs.y , write a linear equation for this information and draw its graph .

Answer 1

Hint: For this use the linear equation in two variables. Polynomial equation \[ax + by + c = 0\] is called the linear equation of first degree and it is nothing but the geometrical representation of a straight line.

Complete step-by-step answer:
The objective of the problem is to write the linear equation of the given information and draw its graph .
Given , the fare of first kilometer is 8
And the subsequent distance is 5
It is also given that total distance covered is taken as x km and total fare as Rs.y
The distance covered after first kilometer becomes\[x - 1\]
At the rate of charges for first kilometer is 8 and the subsequent distance is 5
The total fare becomes \[8\left( 1 \right) + 5\left( {x - 1} \right)\]
On simplifying the above expression we get,
\[\
 = 8 + 5x - 5 \\
 = 5x + 3 \\
\ \]
But the total fare is given that y so
\[\
 \Rightarrow 5x + 3 = y \\
 \Rightarrow 5x - y + 3 = 0.....\left( 1 \right) \\
\ \]
Equation (1) is the required linear equation.
Now , we have to draw the graph of this linear equation .
For this, we have to find the points which satisfies the linear equation
When $x = 0$
That is substitute $x = 0$ in equation (1) , we get
$\
 \Rightarrow 5\left( 0 \right) - y + 3 = 0 \\
 \Rightarrow y = 3 \\
\ $
When $x = 1$
That is substitute in $x = 1$ equation (1) , we get
$\
 \Rightarrow 5\left( 1 \right) - y + 3 = 0 \\
 \Rightarrow y = 8 \\
\ $
When $x = 2$
That is substitute $x = 2$ in equation (1) , we get
$\
 \Rightarrow 5\left( 2 \right) - y + 3 = 0 \\
 \Rightarrow y = 13 \\
\ $
It is enough to take three points .

x	0	1	2
y	3	8	13

Thus , the points $\left( {0,3} \right),\left( {1,8} \right),\left( {2,13} \right)$
Now , plot these points on the graph

Note: For this type of questions first write down the given details and use those to write the linear equation. Then find the points satisfying the given equation . We can also take more than three values. It takes 3 points because to understand the reader easily without any confusion .To draw the linear graph it is enough to take two points.