The slope of the tangent line to the parabola y=4x2+3x+7\displaystyle {y}={4}{x}^{{2}}+{3}{x}+{7} at the point (4,83)\displaystyle {\left({4},{83}\right)} is:  


The equation of this tangent line can be written in the form y=mx+b\displaystyle {y}={m}{x}+{b} where m\displaystyle {m} is:  


and where b\displaystyle {b} is: