Jinx scales very heavily with AD (140% W, 100% R, her Q rocket launcher deals 110% AD damage). She also gets free attack speed with her minigun (130% when maxed) so that she's not that dependant from attack speed items.
Bloodthirster is not only cheaper than Infinity Edge but also gives lifesteal while granting a pretty similar damage output which makes it the first item in the build.
Last Whisper increases her overall damage further while being a very cheap item.
Statikk Shiv is another cheap item. At that point in the game you want to spam your rocket launcher to make use of that 700 range so you need a good attack speed item. Jinx also builds charges very fast.
Infinity Edge is very expensive which makes it the last damage item. The reason you get it is because you want to increase your crit chance further, it's neccessary for any AD carry that builds crit chance because of the passive.
Guardian Angel gives hybrid resistance and a revive passive. Jinx has no escapes so it's not always the best choice for her. When it's on cooldown you mostly want to sell it for a different defensive item.
Blade of the Ruined King is neccessary against HP stackers, it's good on jinx but not better than bloodthirster usually.
Runaan's Hurricane is a very very late game item, it's awesome when you can kite in teamfights, however it does not proc the rocket launcher passive but the bolts proc lifesteal. It's generally good on high range AD carries like Twitch, Caitlyn and Varus. Jinx (700 range) has even more range than Caitlyn (650).

AD marks are good for lane, lifesteal quints are good for sustain, Jinx can push very fast so she will lifesteal a lot when she pushes the lane. Flat armor and magic resistance because most lanes deal hybrid damage.