# Decision Boundary

Learn about the concept of decision boundary.

## Decision boundary for logistic regression

We have just figured out that whenever *z* equals zero, we are in the **decision boundary**. But *z* is given by a linear combination of features *x _{1}* and

*x*. If we work out some basic operations, we arrive at:

_{2}$z \space = \space 0 \space = \space b \space + \space w_1x_1 + \space w_2x_2$

$-w_2x_2 \space = \space b \space + \space w_1x_1$

$x_2 \space = \space -\dfrac{b}{w_2} - \dfrac{w_1}{w_2}x_1$

Given our model (*b*, *w _{1}*, and

*w*), for any value of the first feature (

_{2}*x*), we can compute the corresponding value of the second feature (

_{1}*x*) that sits exactly at the decision boundary.

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