Adding custom header on homepage only

WordPress version: 3.4
Theme: RT-15 (purchased from ThemeForest.net)
Link to theme: https://themeforest.net/item/rttheme-15-premium-wordpress-theme/full_screen_preview/781397

I tried the support page for the theme, but could not get any help.

I’m trying to add a custom header image (640×140) above the slideshow on my static homepage. I want this custom header image to show up only on the homepage.

I understand HTML but I am a total newbie to PHP and thus, I cannot figure out how to add a customer header above the slideshow on my homepage.

I created some CSS:

.homepage-header {
	background: url("https://www.mytesttheme.net/wp-content/themes/yellow/images/homepage-header.jpg") no-repeat;
	width: 640px;
	height: 140px;

Here is the top part of code block for index.php:

<?php
/*
* rt-theme home page
*/
get_header();
?>

	<!-- slider -->
	<?php if(get_option(THEMESLUG."_slider_active") && is_front_page()){	//if slider active and is front page
			//Slider selection
			if(get_option(THEMESLUG.'_home_slider_script')=="" or get_option(THEMESLUG.'_home_slider_script')=="cycle"){
				get_template_part( 'slider', 'home_slider' );
			}else{
				get_template_part( 'nivo-slider', 'home_slider' );
			}
		}
	?>
	<!-- / slider -->

	<!-- home page contents -->

		<?php
		//home pae content
		$home_page=array(
		    'post_type'=> 'home_page',
		    'post_status'=> 'publish',
		    'ignore_sticky_posts'=>1,
		    'showposts' => 1000,
		    'orderby'=> 'date',
		    'order' => 'ASC',
		    'cat' => -0,
		);

and here bottom part of code from header.php:

<!-- content -->
	<div id="content">
		<?php if(	(( get_option(THEMESLUG."_slider_active") && is_front_page()) || is_front_page() ) && (!get_option(THEMESLUG.'_remove_curvs')) ) echo '<div class="slider_cover"></div>';  ?>
		<div class="content_top <?php if(get_option(THEMESLUG.'_remove_curvs') && !is_front_page()):?>no_curv<?php endif;?> <?php if(get_option(THEMESLUG.'_remove_curvs') && is_front_page()):?>no_curv_home<?php endif;?> "></div>
		<div class="content">

I’m sure it’s simple code, but everything I tried fails to even show the image at all.

Thanks for your time.