ai - Enemy movement in straight line to player in chase game

I'm creating a game where the enemies spawn randomly on a map then move towards the player every frame at a random speed. The map has no obstacles so the enemies should always move in a straight line. I wrote the movement function a few times but no matter what the enemies always hit 0, 45, 90, 135, 180, 225, 270, 315 angles but never a straight line. Here is an example of the code:

    base_speed = random();

    diff_x = abs(enemy_y_pos - player_x_pos);
    diff_y = abs(enemy_x_pos - player_y_pos);
     if (diff_x > diff_y) {
      y_speed = base_speed;
     } else if (diff_y > diff_x) {
      x_speed = base_speed;

     }

     if (enemy_x_pos < player_x_pos) {
      velocity.x = x_speed;
     } else if (enemy_x_pos > player_x_pos) {
      velocity.x = -x_speed;
     } else {
      velocity.x = 0;
     }


     if (enemy_y_pos < player_y_pos) {
      velocity.y = y_speed;
     } else if (enemy_y_pos > player_y_pos) {
      velocity.y = -y_speed;
     } else {
            velocity.y = 0;
    }

    enemy_x_pos = enemy_x_pos + velocity.x;
    enemy_y_pos = enemy_y_pos + velocity.y;

This is my first attempt at game programming. I guessing it's should use algorithm like Bresenham’s Line( http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm) but my attempts to implement have the same issue. How do I make enemies move in a straight line?

Answer

Bresenham's line algorithm was developed for fast drawing lines without using floating point operations (integer operations are faster). It is very interesting historicaly but not very good solution for a game (especialy because you cannot specify speed).

When doing a 2D movement use always vectors. This will do all the stuff for you. Sometimes is algebra just wonderful.

Vec2d playerPos;
Vec2d direction; // always normalized
float velocity;

update()

{
   direction = normalize(playerPos - enemyPos);
   playerPos = playerPos + direction * velocity;
}

There will be some vector2D class for your target language for sure.