Suppose I have a toy dataset like following
Age height label 20 5 young 40 6 old 10 4 young 50 6 old 45 7 old
Depending on the toy dataset I tried to draw a graph
The dataset is a linearly separable dataset. Therefore, the purple, red, and yellow lines all are able to differentiate the two classes. I am thinking about the support vector machine concept. If there are two features support vector machine draw a line to separate two classes. I went through various videos and tutorials. Everyone try to busy explain if there is a line how could I determine that the points are in the positive side or in the negative sides. They also use the equation $$W^TX$$ to determine which side the point should be. However, some videos draw the separation line through origin of the coordinate, some draw lines just below of above the origin.
I would like to know which line I need to consider as the separator of two classes.
I draw a line randomly. If the line pass through the origin the equation of the line will be y=mx+c, where say, c =0, m=-1. Afterward, we take each point and find out which side it lies depending on $$W^TX$$
Based on the above idea if I draw a line pass through the origin(pink line), all points lie on one side of the line. So, how could I classify the data into two classes?