are explanatory variables in multiple linear regression slopes? In simple linear regression the formula is: $y = m \cdot x + b$.
 When there are multiple independent variables: $y = b_0 + b_1 \cdot x_1 + b_2 \cdot x_2 + \ldots $

I know that $x_1,x_2,\ldots $ represents different independent variables but what exactly is $b_1,b_2,\ldots$?
They are the coefficients.

Suppose you keep the other variable fixed besides $x_1$. How much does increasing a single unit of $x_1$ would affect $y$? According to the formula, it would change by $b_1$. Similarly for the other variables.