\(y=5x+2=5x-15+15+2=5(x-3)+17\implies y-17=5(x-3)\)
The tangent line to \(f(x)\) at \(x=c\), given the slope \(f'(c)\) at \(x=c\), is
\(y-f(c)=f'(c)(x-c)\)
In this case, \(c=3\). Matching this with the equation above, you find that \(f(c)=17\) and \(f'(c)=5\).
