How does tf.estimator.LinearClassifier calculate the y value to be plotted on feature space?

I’ve come across this article and on page 5, it says:

General input/output for SVMs just like for neural nets, but for one important addition… Input: set of (input, output) training pair samples; call the input sample features x1, x2…xn, and the output result y. Typically, there can be lots of input features xi. Output: set of weights w (or wi), one for each feature, whose linear combination predicts the value of y. (So far, just like neural nets…)

It mentions that the y value is calculated through the LC of the weights? Does this mean that x_i • w_i would give me the y value for x_i ∈ X ? If so, how can i calculate the weights w?

If possible, could someone ELI5 this formula on pg 8 for me:

w•xi+b ≥ +1 when yi =+1 w•xi+b ≤ -1 when yi = –1


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