posts to pull from subcategory

I have been working with a programmer on a custom theme. It is almost right but i want the home page to pull from posts within a subcategory of a category. here is the code in the functions.php

<?php $prim_post_id = get_option('home_prime_slider'); ?>
                    	<th scope="row"><label for="pri_slider">Select The Category For Slider</label></th>
                    	<td>
                        <select name="slider_cat" id="slider_cat">
                        	<option>SELECT</option>
                        	<?php  // Get all categories
								$slider_cat_id = get_option('slider_category');
								$args = array(
									'type' => 'post',
									'taxonomy'=> 'category'
								);
								$categories = get_categories( $args );
								foreach ( $categories as $cat ):
									if( $cat->term_id == $slider_cat_id ):
                            		echo '<option value="'.$cat->term_id.'" selected="selected">'.$cat->name.'</option>';
									else:
									echo '<option value="'.$cat->term_id.'">'.$cat->name.'</option>';
									endif;
								endforeach;
							?>

can anyone guide me as to how to adapt this to include subcategories of the main category?