Paying a larger % downpayment up front

[Mark Dolan]

Hi guys, I am new to the site and I am exploring the possibilities of investing in a rental property over the coming year. My biggest concern however is that I may struggle to get approved of a mortgage based on my low income reflected over the past few years. I am wondering if lenders allow you to pay a larger down payment to minimize the amount that you would need to borrow. I figure if people can buy houses with cash they perhaps they allow for something like this. Sorry if this is a silly question, I am still totally new to this and trying to figure out the basics. 

Thanks!!