Sample HD wallet for Ethereum

ethereumHD.js

const bip39 = require("bip39"); // mnemonic generator
const hdkey = require("hdkey"); // wallet lib
const ethUtil = require("ethereumjs-util"); // Used here for public address and public key generation

const mnemonic = bip39.generateMnemonic(); // generates string
const seed = bip39.mnemonicToSeedSync(mnemonic).toString('hex'); // creates seed for wallet

const root = hdkey.fromMasterSeed(seed);

const masterPrivateKey = root.privateKey.toString('hex');

// 1st Address
var addrNode = root.derive("m/44'/60'/0'/0/0"); // "m / purpose' / coin_type' / account' / change / address_index"
var pubKey = ethUtil.privateToPublic(addrNode._privateKey);
var addr = ethUtil.publicToAddress(pubKey).toString('hex');
var address = ethUtil.toChecksumAddress(addr);

// 2nd Address
var addrNode = root.derive("m/44'/60'/0'/0/1"); // "m / purpose' / coin_type' / account' / change / address_index"
var pubKey = ethUtil.privateToPublic(addrNode._privateKey);
var addr = ethUtil.publicToAddress(pubKey).toString('hex');
var address = ethUtil.toChecksumAddress(addr);

But I can't seem to link the seed phrase with the private key here.