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If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

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The equations of the given lines are
y = 3x + 1 ……………………..… (1)
2y = x + 3 ……………………… (2)
y = mx + 4 …………………….. (3)
Slope of line (1), m1 = 3
Slope of line (2), m2 = 1/2
Slope of line (3), m3 = m

It is given that lines (1) and (2) are equally inclined to line (3). This means that the angle between lines (1) and (3) equals the angle between lines (2) and (3).

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