Question

how to identify whether a question is in direct or inverse proportion

Answer 1

Answer:

ᴅɪʀᴇᴄᴛ ᴘʀᴏᴘᴏʀᴛɪᴏɴ

ᴛᴡᴏ ǫᴜᴀɴᴛɪᴛɪᴇs ᴀ ᴀɴᴅ ʙ ᴀʀᴇ sᴀɪᴅ ᴛᴏ ʙᴇ ɪɴ ᴅɪʀᴇᴄᴛ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪғ ᴛʜᴇʏ ɪɴᴄʀᴇᴀsᴇ ᴏʀ ᴅᴇᴄʀᴇᴀsᴇ ᴛᴏɢᴇᴛʜᴇʀ. ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇɪʀ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴠᴀʟᴜᴇs ʀᴇᴍᴀɪɴs ᴄᴏɴsᴛᴀɴᴛ. ᴛʜɪs ᴍᴇᴀɴs ᴛʜᴀᴛ,

• ᴀ/ ʙ = ᴋ
• ᴡʜᴇʀᴇ ᴋ ɪs ᴀ ᴘᴏsɪᴛɪᴠᴇ ɴᴜᴍʙᴇʀ, ᴛʜᴇɴ ᴛʜᴇ ǫᴜᴀɴᴛɪᴛɪᴇs ᴀ ᴀɴᴅ ʙ ᴀʀᴇ sᴀɪᴅ ᴛᴏ ᴠᴀʀʏ ᴅɪʀᴇᴄᴛʟʏ.
• ɪɴ sᴜᴄʜ ᴀ ᴄᴀsᴇ ɪғ ᴛʜᴇ ᴠᴀʟᴜᴇs b1, b2 of b ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴛᴏ ᴛʜᴇ ᴠᴀʟᴜᴇs a1, a2 ᴏғ ᴀ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ ᴛʜᴇɴ ɪᴛ ʙᴇᴄᴏᴍᴇs;
• a1//b1 = a2 /b2

ᴛʜᴇ ᴅɪʀᴇᴄᴛ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪs ᴀʟsᴏ ᴋɴᴏᴡɴ ᴀs ᴅɪʀᴇᴄᴛ ᴠᴀʀɪᴀᴛɪᴏɴ.

ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴ sʏᴍʙᴏʟ

• ᴛʜᴇ sʏᴍʙᴏʟ ᴜsᴇᴅ ᴛᴏ ʀᴇᴘʀᴇsᴇɴᴛ ᴛʜᴇ ᴅɪʀᴇᴄᴛ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪs “∝”.
• ᴄᴏɴsɪᴅᴇʀ ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ,
• ᴀ ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ʙ

ᴛʜɪs ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴜsɪɴɢ ᴛʜᴇ sʏᴍʙᴏʟ ᴀs:

• ᴀ ∝ ʙ
• ᴄᴏɴsɪᴅᴇʀ ᴛʜᴇ ᴏᴛʜᴇʀ sᴛᴀᴛᴇᴍᴇɴᴛ, ᴀ = 2b
• ɪɴ ᴛʜɪs ᴄᴀsᴇ, ɪᴛ sʜᴏᴡs ᴛʜᴀᴛ ᴀ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ʙ, ᴀɴᴅ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴏɴᴇ ᴠᴀʀɪᴀʙʟᴇ ᴄᴀɴ ʙᴇ ғᴏᴜɴᴅ ɪғ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴏᴛʜᴇʀ ᴠᴀʀɪᴀʙʟᴇ ɪs ɢɪᴠᴇɴ

ɪɴᴠᴇʀsᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴ

ᴛᴡᴏ ǫᴜᴀɴᴛɪᴛɪᴇs ᴀ ᴀɴᴅ ʙ ᴀʀᴇ sᴀɪᴅ ᴛᴏ ʙᴇ ɪɴ ɪɴᴠᴇʀsᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪғ ᴀɴ ɪɴᴄʀᴇᴀsᴇ ɪɴ ᴛʜᴇ ǫᴜᴀɴᴛɪᴛʏ ᴀ, ᴛʜᴇʀᴇ ᴡɪʟʟ ʙᴇ ᴀ ᴅᴇᴄʀᴇᴀsᴇ ɪɴ ᴛʜᴇ ǫᴜᴀɴᴛɪᴛʏ ʙ, ᴀɴᴅ ᴠɪᴄᴇ-ᴠᴇʀsᴀ. ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴛʜᴇɪʀ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴠᴀʟᴜᴇs sʜᴏᴜʟᴅ ʀᴇᴍᴀɪɴ ᴄᴏɴsᴛᴀɴᴛ. sᴏᴍᴇᴛɪᴍᴇs, ɪᴛ ɪs ᴀʟsᴏ ᴋɴᴏᴡɴ ᴀs ɪɴᴠᴇʀsᴇ ᴠᴀʀɪᴀᴛɪᴏɴ

• ᴛʜᴀᴛ ɪs, ɪғ ᴀʙ = ᴋ,
• ᴛʜᴇɴ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ sᴀɪᴅ ᴛᴏ ᴠᴀʀʏ ɪɴᴠᴇʀsᴇʟʏ.
• ɪɴ ᴛʜɪs ᴄᴀsᴇ, ɪғ b1, b2 ᴀʀᴇ ᴛʜᴇ ᴠᴀʟᴜᴇs ᴏғ ʙ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴛᴏ ᴛʜᴇ ᴠᴀʟᴜᴇs a1, a2 ᴏғ ᴀ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ
• ᴛʜᴇɴ a1 b1 = a2 b2 or a1/a2 = b2 /b1

ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ ‘ᴀ ɪs ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ʙ ɪs ᴡʀɪᴛᴛᴇɴ ᴀs

• a ∝ 1/b
• ʜᴇʀᴇ, ᴀɴ ᴇǫᴜᴀᴛɪᴏɴ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ ɪɴᴠᴏʟᴠᴇs ᴛʜᴇ ɪɴᴠᴇʀsᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴs ᴛʜᴀᴛ ᴄᴀɴ ʙᴇ ᴜsᴇᴅ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴏᴛʜᴇʀ ᴠᴀʟᴜᴇs.