the taxi fare in acity is nas follows :for the first two kilometers ,the fare is Rs.12and for the subsequent distance it is Rs.5 per kilometre. taking the dista

Question

the taxi fare in acity is nas follows :for the first two kilometers ,the fare is Rs.12and for the subsequent distance it is Rs.5 per kilometre. taking the distance as x and total fare as Rs.y , write alinear equation for this information and draw its graph

Answer 1

Writing the equation as y = Mx + b

lets see what we already know.

M is how many Rs per km. The problem says that is 5 Rs/km. 

So we can start with y = 5x + b

 

what is the value of b?

Find out by putting in 0 km.

As soon as you step in the taxi, y = 12 Rs., So b = 12.

 

now we have y = 5x + 12

 

But it’s wrong, because the fare is 12 for x =0, x=1, and x=2.

 

Also, those first two kilometers are free, it‘s only km beyond two that cost.

 

so let’s change it to y = 5(x-2) + 12

 

This is now accurate for x=2 and above, but still not accurate for x<= 2.

 

So the function is really

y = 12 , x<= 2

y = 5(x-2) + 12, x>2

 

so this function is not linear, it is “piecewise linear”. I’ll bet you know how to graph it.