Question

The bus fare in a city is as follows. For the first five kilometres the fare is `10 and for the subsequent distance it is `2 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. What will the bus fare for 10 km and 19 km.​

Answer 1

$\: \: \: \: \: \: \:$

ǫᴜᴇsᴛɪᴏɴ:

ᴛʜᴇ ʙᴜs ғᴀʀᴇ ɪɴ ᴀ ᴄɪᴛʏ ɪs ᴀs ғᴏʟʟᴏᴡs. ғᴏʀ ᴛʜᴇ ғɪʀsᴛ ғɪᴠᴇ ᴋɪʟᴏᴍᴇᴛʀᴇs ᴛʜᴇ ғᴀʀᴇ ɪs `10 ᴀɴᴅ ғᴏʀ ᴛʜᴇ sᴜʙsᴇǫᴜᴇɴᴛ ᴅɪsᴛᴀɴᴄᴇ ɪᴛ ɪs `2ᴘᴇʀ ᴋᴍ. ᴛᴀᴋɪɴɢ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴄᴏᴠᴇʀᴇᴅ ᴀs x ᴋᴍ ᴀɴᴅ ᴛᴏᴛᴀʟ ғᴀʀᴇ ᴀs `ʏ, ᴡʀɪᴛᴇ ᴀ ʟɪɴᴇᴀʀ ᴇǫᴜᴀᴛɪᴏɴ ғᴏʀ ᴛʜɪs ɪɴғᴏʀᴍᴀᴛɪᴏɴ ᴀɴᴅ ᴅʀᴀᴡ ɪᴛs ɢʀᴀᴘʜ. ᴡʜᴀᴛ ᴡɪʟʟ ᴛʜᴇ ʙᴜs ғᴀʀᴇ ғᴏʀ 10 ᴋᴍ ᴀɴᴅ 19 ᴋᴍ.

Solution:

Complete step-by-step answer:

Given that,

The fare for the first kilometre is Rs. 8 and after that, the fare is Rs. 5 per km.

According to the question,

Total distance covered = x km = 1 + (x-1) km.

Total fare = Rs. y.

The fare of first kilometre = Rs. 8.

The subsequent fare = Rs. 5 per km.

So, we can write these statements in the form of equation as:

• 8(1) + 5(x- 1) = y
• 8+ 5x - 5 = y
• 5x-y+3= 0

Now, we have to draw the graph for this linear equation.

So, we have to find out the points that will satisfy the given equation.

When x = 0,

• y = 5(0) + 3 = 3.
• When x = 1,
• y = 5(1) + 3
• y = 8.

When x = 2,

• y = 5(2) + 3
• y = 13.

Thus, the points that satisfy equation (i) are ( 0,3 ), ( 1,8 ), ( 2,13 ) and so on.

Now, we will plot these points on the graph.

ʜᴏᴘᴇ ᴛʜɪs ʜᴇʟᴘs ʏᴏᴜ!!!

#ʙᴇ ʙʀᴀɪɴʟʏ!