Consider this simple case where two triangle vertices connected by an edge have the same color (in this case, black). Here, the color of a point inside the triangle is the single linear combination of blue (from vertex C) and black (from the edge b-a). The interpolation weights are determined by the distance from the point X to the b-a edge. This is just linear interpolation like from the previous slide!
But now the question is how to we extend this notion of linearly interpolation of three values in 1D to interpolation of three values in 2D.