As a Software Developer, your basic intuition would be to consume the information of the geographic coordinates in the 'longitude/latitude' order, i.e., the 'x/y' order, which would be the most common way to distribute data.
However, the traditional way of "displaying" the information in geographic and cartographic systems is the opposite — 'latitude/longitude' (y/x). Also, according to the international standard for the representation of latitude, longitude and altitude for geographic point locations; ISO 6709: Standard representation of geographic point location by coordinates: it should be "latitude/longitude".
Note that the standard only talks about the representation (data display), and nothing about the communication (data interchange), of the coordinates. There is a bit of history to this.
An excerpt from History of longitude
Finding an accurate and reliable method of determining longitude took centuries of study, and involved some of the greatest scientific minds in human history.
Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon (i.e. at its highest point) with the aid of a table giving the sun's declination for the day, or from many stars at night.
In order to avoid problems with not knowing one's position accurately, navigators have, where possible, relied on taking advantage of their knowledge of latitude. They would sail to the latitude of their destination, turn toward their destination and follow a line of constant latitude. This was known as running down a westing (if westbound, easting otherwise).
This was one of the primary reasons why latitude took prominence over latitude when geographic coordinates were communicated among cartographers in the pre-digital era, as its calculation was relatively way more easier.
The standard evolved the way it did, as it seriously took into consideration, this one fact — Since navigators have traditionally used the 'latitude/longitude' (y/x) order, a change in the order could mean a compromise in safety.
GeoTools, an open source Java library which provides tools for dealing with geospatial data; has a document briefly explaining the history of this problem, from a software development perspective; and it is a damn interesting read.