Question

12. 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.​

Answer 1

Let the total distance be x km

and total cost be y

now, 10rs for 1st km, and 4Rs. per km for rest

so,

y=1(10)+4(x-1)

y=4x+6,

 

sub,

x=-2,y=-2

x=-1, y=2

 

so plot points (-2,-2),(-1,2)

scale : 1cm = 1 unit on both axis

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

Let total distance covered = x km

Total Cost for the distance covered = ₹ y

Now The Auto Rickshaw fare in a city is charged ₹ 10 for the first kilometer

Also The Auto Rickshaw fare in a city is charged ₹ 4 per kilometer for subsequent distance covered

As the total distance covered = x km

So the charge per kilometer for the remaining (x-1) kilometers is ₹ 4

So total charge$= 10 + 4 \times (x - 1) = 10 + 4x - 4 = 4x + 6$

Hence $y = 4x + 6$

$\therefore \: 4x - y = - 6$

Which is the required linear equation

The obtained linear equation can be rewritten as

$\displaystyle \: \frac{x}{ - \frac{3}{2} } + \frac{y}{6} = 1$

Which is in intercept form

$\displaystyle\textcolor{green}{Please \: check \: the \: attachment \: for \: the \: graph \: }$