Find the relation between $a$ and $b$ so that the function defined by\\ $f(x)=\begin{cases}ax+1& \text{if}\hspace{.2cm} x \leq 4\\ bx+4,& \text{if}\hspace{.2cm} x>4 \end{cases}$ is continuous at $x=4$ then

$a-b=3/4$

$\lim_{x \to 4+}f(x)=\lim_{x \to 4}bx+4=4b+4$ ,$\lim_{x \to 4-}f(x)=\lim_{x \to 4}ax+1=4a+1$ and $f(4)=4b+4$. In order $f$ to be continuous at $x=4$ we must have$4b+4=4a+1$. Hence $a-b=3/4$.