How to restrict movement on the y axis

Im trying to get it to where my enemy will follow the player. The one problem is that it moves up no matter what I do.

my script c#

using UnityEngine;
using System.Collections;

public class Enemy : MonoBehaviour {

public Transform target;

public float distance;

public float lookAtDistance;

void Start () {

}

// Update is called once per frame
void Update () {

	distance = Vector3.Distance(target.position, transform.position);

	if (lookAtDistance > distance) {
		transform.position = Vector3.MoveTowards (transform.position, target.transform.position, 0.03f);
	}
	
}

}

Vector3 temp = new Vector3 ( target.transform.position.x, transform.position.y, target.transform.position.z)

transform.position = Vector3.MoveTowards (transform.position, temp , 0.03f);

Something like that. Its a starting point anyway.

Create a new position with the same x and z as your target and the same y as your enemy.

var newPos = target.transform.position;
newPos.y = transform.position.y;

transform.position = Vector3.MoveTowards (transform.position, newPos, 0.03f);

59268-screen-shot-2015-12-03-at-84742-am.png