Convert latitude/longitude point to a pixels (x,y) on mercator projection

I'm trying to convert a lat/long point into a 2d point so that I can display it on an image of the world-which is a mercator projection.

I've seen various ways of doing this and a few questions on stack overflow-I've tried out the different code snippets and although I get the correct longitude to pixel, the latitude is always off-seems to be getting more reasonable though.

I need the formula to take into account the image size, width etc.

I've tried this piece of code:

double minLat = -85.05112878;
double minLong = -180;
double maxLat = 85.05112878;
double maxLong = 180;

// Map image size (in points)
double mapHeight = 768.0;
double mapWidth = 991.0;

// Determine the map scale (points per degree)
double xScale = mapWidth/ (maxLong - minLong);
double yScale = mapHeight / (maxLat - minLat);

// position of map image for point
double x = (lon - minLong) * xScale;
double y = - (lat + minLat) * yScale;

System.out.println("final coords: " + x + " " + y);

The latitude seems to be off by about 30px in the example I'm trying. Any help or advice?

Update

Based on this question:Lat/lon to xy

I've tried to use the code provided but I'm still having some problems with latitude conversion, longitude is fine.

int mapWidth = 991;
int mapHeight = 768;

double mapLonLeft = -180;
double mapLonRight = 180;
double mapLonDelta = mapLonRight - mapLonLeft;

double mapLatBottom = -85.05112878;
double mapLatBottomDegree = mapLatBottom * Math.PI / 180;
double worldMapWidth = ((mapWidth / mapLonDelta) * 360) / (2 * Math.PI);
double mapOffsetY = (worldMapWidth / 2 * Math.log((1 + Math.sin(mapLatBottomDegree)) / (1 - Math.sin(mapLatBottomDegree))));

double x = (lon - mapLonLeft) * (mapWidth / mapLonDelta);
double y = 0.1;
if (lat