Thank you for the clarification! Super helpful. To further clarify, a simple linear regression model has the form y = b + mX, whereas a multiple linear regression model has the form y = b + (m_1)(X_1) + (m_2)(X_2) + ... + (m_p)(X_p), where m_1, for instance, is the coefficient applied to the first predictor (height, for example), m_2 is the coefficient applied to the second predictor (weight, for example), and so on.*
You can imagine simplifying this long equation by combining all the m's into a vector and all the X's into a vector and then taking the dot product, or you can just think of it as a long equation like the one I wrote out above.
*(As a small side note, these two equations that I wrote out also have another parameter, which is called the error, but I choose to leave that out so as to keep things simple.)