Math, asked by coolie88, 1 month ago

The auto rickshaw fare in a city is charged Rs 18 for the first kilometer and a rate of Rs 6 per kilometer for subsequent distance covered . write the linear equation to express the above statement. Also Draw the graph of the linear equation

Answers

Answered by mathdude500
10

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

Given that,

The auto rickshaw fare in a city is charged Rs 18 for the first kilometer and a rate of Rs 6 per kilometer for subsequent distance covered .

Let assume that

Total distance covered be x km.

Total fare be Rs y

So, According to statement

\rm \: y = 1 \times 18 + (x - 1) \times 6 \\

\rm \: y = 18 + 6x - 6 \\

\bf\implies \: \: y = 12 + 6x \\  \\

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

\rm \: y = 12 + 6 \times 0 \\  \\

\rm \: y = 12 + 0 \\  \\

\bf\implies \:\: y = 12 \\  \\

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

\rm \: y = 12 + 6 \times 1 \\  \\

\rm \: y = 12 + 6  \\  \\

\bf\implies \:\: y = 18  \\  \\

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

\rm \: y = 12 + 6 \times 2 \\  \\

\rm \: y = 12 + 12 \\  \\

\bf\implies \:y = 24 \\  \\

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 12 \\ \\ \sf 1 & \sf 18 \\ \\ \sf 2 & \sf 24 \end{array}} \\ \end{gathered} \\

➢ Now draw a graph using the points (0 , 12), (1 , 18) & (2 , 24)

➢ See the attachment graph.

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