What is the technique to make a bunch of straight lines appear as if they are 1 straight line?

In 2D graphics, 4 straight lines can be drawn; horizontal, vertical, oblique-right, and oblique left.

The lines in red and blue are represented by y = x and y = -x respectively. Attempting to graph something different than that such as y = 2x requires drawing multiple straight lines:

That, despite looking like 1 straight line is made up of multiple vertical straight lines; in order to reveal the visual trick, all we have to do is to zoom in to the picture:

I want to implement the technique using c++ and winapi, but what is that technique?

Generally, there are two types of lines, and the method you use differs between them:

• thin lines, which are drawn directly at the pixel level
• thick lines, which are drawn by combining primitives like triangles, which are rendered using rasterization

Thin Lines

Two rasterized lines. The colored pixels are shown as circles. Above: monochrome screening; below: Gupta-Sproull anti-aliasing - by Phrood~commonswiki

Drawing thin lines happens using specialized algorithms. Usually, the aim is to draw a line which is only one pixel wide.
The algorithm depends on your goals:

• Bresenham's line algorithm is a popular choice for pixel-perfect, very thin lines with no anti-aliasing
• The Gupta and Sproll algorithm produces thin, but smooth (anti-aliased) lines
• ...

See also: Line drawing algorithm on Wikipedia

Thick Lines

These are easier and harder to render at the same time.
If you don't have to worry about line endings and corners, you just create a quadliteral around the line, and render it using rasterization like everything else.

However, rendering corners and endings requires using multiple primitives typically:

A thick line with a rounded corner consisting of quads, triangles, and a circle - by @japreiss

The red line that you've shared looks like a thick line, because it is multiple pixels thick.

See also: https://stackoverflow.com/q/22483198/5740428