Autorikshaw fare in a city is charged Rs., 10 for first kilometer and @ Rs., 4 per kilometer for sub

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4. Linear Equations in Two Variables

medium

The Autorikshaw fare in a city is charged $Rs.\, 10$ for the first kilometer and @ $Rs.\, 4$ per $kilometer$ for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation.

Option A

Option B

Option C

Option D

Solution

Let the total distance covered be $x\, km$ and the fare charged $\operatorname{Rs} \,y .$ Then for the first $km ,$ fare charged is $Rs.\, 10$ and for remaining $(x-1)$ $km$ fare charged is $\operatorname{Rs}.\, 4(x-1)$

Therefore, $y=10+4(x-1)=4 x+6$

The required equation is $y=4 x+6$. Now, when $x=0, y=6$ and when $x=-1, y=2 .$ The graph is given in $Fig.$

Standard 9

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The Autorikshaw fare in a city is charged $Rs.\, 10$ for the first kilometer and @ $Rs.\, 4$ per $kilometer$ for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation.

Solution

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