ageron / ageron/handson-ml2

Chap5 Under the Hood

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In the section "Training Objective" on page 196, why does dividing the slope by 2 will multiply the margin by 2? Does the margin mean horizontal distance rather than perpendicular distance? And why do we care about the $x$ coordinate of the intersection between the slope $w_1$ and $y = \pm1$?

I guess my question really is how did we get this plot.

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