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