Question

The taxi fare in a city is as follows: For the first kilometer, the fare is 16 and for the subsequent distance it is 10 per km. Taking the distance covered as x km and total fare as y, write a linear equation for this information, and draw its graph.​

Answer 1

$\green{\large\underline{\sf{Solution-}}}$

Given that,

• For the first kilometer, the fare is 16 and for the subsequent distance it is 10 per km.

• Taking the distance covered as x km and total fare as y

So,

• Fare for first km = 16

• Fare for (x - 1) km = 10(x - 1) = 10x - 10

Thus,

Total fare is

$\rm :\longmapsto\:y = 16 + 10x - 10$

$\red{\rm :\longmapsto\:y = 10x + 6}$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y = 10 \times 0 + 6$

$\rm :\longmapsto\:y = 0 + 6$

$\bf\implies \:y = 6$

Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:y = 10 \times 1 + 6$

$\rm :\longmapsto\:y = 10 + 6$

$\bf\implies \:y = 16$

Substituting 'x = 2' in the given equation, we get

$\rm :\longmapsto\:y = 10 \times 2 + 6$

$\rm :\longmapsto\:y = 20+ 6$

$\bf\implies \:y = 26$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 1 & \sf 16 \\ \\ \sf 2 & \sf 26 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.