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 fare as Rs. $y$, write a linear equation for this information, and draw its graph.

Answer 1

Step 1: Let us assume

Distance covered as $x$ km and total fare as $₹y$

Fare for the first kilometer $=8$ per km

Fare after the first $1$ km $=₹5$ per km

Let $x$ be the total distance, then the distance after one km will be $=(x-1)$ km

Hence, Fare after the first km $=5(x-1)$

Step 2: Find the total fare

So, in equation form, we can conclude that,

The total fare $=$ Fare of first km $+$ fare after the first km

$$\begin{gathered} y=8+5(x-1) \\ y=8+5(x-1) \\ y=8+5x–5 \\ y=5x+3 \end{gathered}$$

Step 3: Draw the graph

To draw the graph $y=5x+3$, we need at least two solutions to the equation.

We can check that when,$x=0,y=3,$ and $x=-1,y=-2$are solutions of the given equation.

So, we can use the following table to draw the graph :

$x$	$y$
$0$	$3$
$-\frac{3}{5}$	$0$

The points to be plotted are $(0,3)$ and $(-\frac{3}{5},0)$

Hence, the required answer is shown above.