How is the direction of intercept determined? Let's say I have a equation like as below (linear regression)
Y = intercept + x1+x2+x3...xn
intercept = 30
positive coeff sum = 40
negative coeff sum = -10
So, the final outcome becomes like as below
30 + 40 - 10 = 60
My question is why does intercept have to be +30?
It could have been -30 as well?
Whether logistic or linear regression, how is the sign of intercept determined?
Does intercept only take positive values always?

It is determined by the estimation method you select. In OLS, the regression parameters $\hat\beta_{OLS}$ are determined by the following.
$$
\hat\beta_{OLS}=(X^TX)^{-1}X^Ty
$$
Whatever the result of that calculation turns out to be is the answer.
Logistic regression does not have a closed-form equation for its parameter vector, but it can be calculated as the parameter vector that minimizes the crossentropy loss function (same as how OLS minimizes the square loss function, which turns out to be the same as the $\hat\beta_{OLS}$ above). Whatever the intercept value is in the parameter vector is the intercept in the logistic regression; any real number is possible.
