Let $a$ and $b$ be real numbers. The function $h(x)=ax+b$ satisfies $h(1)=5$ and $h(-1)=1$.  What is $h(6)$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a$ and $b$ be real numbers. The function $h(x)=ax+b$ satisfies $h(1)=5$ and $h(-1)=1$.  What is $h(6)$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
15
Let $a$ and $b$ be real numbers. The function $h(x)=ax+b$ satisfies $h(1)=5$ and $h(-1)=1$.  What is $h(6)$?
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