Question

The taxi fare in a city is as follows: For the first kilometre, 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

$x$	$0$	$1$	$2$
$y$	$3$	$8$	$13$

Taxi fare for first kilometer $=$ Rs. $8$

Taxi fare for subsequent distance $=$ Rs. $5$

Total distance covered $=x$

Total fare $=y$

Since the fare for first kilometer $=$ Rs.$8$

According to problem,

Fare for $(x–1)$ kilometer $=$ $5(x-1)$

So, the total fare $y=5(x-1)+8$

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

$\Rightarrow y=5x–5+8$

$\Rightarrow y=5x+3$

$Hence$, $y=5x+3$ $\text{is the required linear equation.}$

Now the equation is

$y=5x+3$ ...(1)

Now, putting the value $x=0$ in (1)

$y=5\times 0+3$

$y=0+3=3$ So the solution is $(0,3)$

Putting the value $x=1$ in (1)

$y=5\times 1+3$

$y=5+3=8$. So the solution is $(1,8)$

Putting the value $x=2$ in (1)

$y=5\times 2+3$

$y=10+3=13$. So the solution is $(2,13)$