Question

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

Answer 1

Fare for the first kilometer = $Rs.8$

Fare for subsequent distance thus covered = $Rs.5$

Total distance covered = $xkm$

Therefore, fare that should be charged for $xkm$ = Fare for first kilometer + Fare for $(x-1)km$

$\Rightarrow 1\times 8+(x-1)\times 5$

$=8+5x-5$

$=Rs.5x+3$

Now, ATQ,

$Rs.(5x+3)=Rs.y$ or $5x+3=y$

Thus, the required linear equation is $5x+3=y$

Now, if, $x$ assumes the following values, we get the values of $y$.

$\begin{array}{cccc}x& 0& 1& 2\\ y& 3& 8& 13\end{array}$

Thus, the graph of the given linear equation is