Merging two line equations having similar angle into a new one

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I would like to merge two lines having a y = mx + b equation with very close angles. I am simply comparing their angle difference, then I create a new line passing through the middle of these by calculating their m and b average.

This method succeeds when the algorithm encounters two lines with positive values.

The segment on the right has it's m variable set to 0.034, and b variable set to 109.49. The segment on the left has it's m variable set to 0.017, and b variable set to 128.72.

The averaging method gives a result of m being 0.026 and b with the value of 119.105.

But I am actually stuck in the case where there are two diagonal lines, where one of them has a negative m variable.

The segment on the top right has it's m variable set to 26.837, and b variable set to -44172.254. The segment on the bottom left has it's m variable set to -19.648, and b variable set to 29264.59.

The averaging method gives a result of m being 3.5945 and b with the value of -7453.8324.

Is there a more efficient method of solving this problem ?