You can draw two triangles:
// Draws a line between (x1,y1) - (x2,y2) with a start thickness of t1 and
// end thickness t2.
void DrawLine(float x1, float y1, float x2, float y2, float t1, float t2)
{
float angle = atan2(y2 - y1, x2 - x1);
float t2sina1 = t1 / 2 * sin(angle);
float t2cosa1 = t1 / 2 * cos(angle);
float t2sina2 = t2 / 2 * sin(angle);
float t2cosa2 = t2 / 2 * cos(angle);
glBegin(GL_TRIANGLES);
glVertex2f(x1 + t2sina1, y1 - t2cosa1);
glVertex2f(x2 + t2sina2, y2 - t2cosa2);
glVertex2f(x2 - t2sina2, y2 + t2cosa2);
glVertex2f(x2 - t2sina2, y2 + t2cosa2);
glVertex2f(x1 - t2sina1, y1 + t2cosa1);
glVertex2f(x1 + t2sina1, y1 - t2cosa1);
glEnd();
}