7. If the graph of the inverse proportion function $y=\frac{k}{x}$ intersects the graph of the linear function $y=a x+b$ at points $A(-2, m)$ and $B(5, n)$, then the value of $3 a+b$ is

保留了源文本的换行和格式。
Ni.7.0.
Since points $A(-2, m)$ and $B(5, n)$ lie on the graph of an inverse proportion function, we have 
$$
\left\{\begin{array}{l}
m=-\frac{k}{2}, \\
n=\frac{k}{5} .
\end{array}\right.
$$

Since points $A(-2, m)$ and $B(5, n)$ also lie on the line $y=a x+b$, we get
$$
\left\{\begin{array}{l}
m=-2 a+b \\
n=5 a+b
\end{array}\right.
$$

Thus, 
$$
\left\{\begin{array}{l}
-2 a+b=-\frac{k}{2}, \\
5 a+b=\frac{k}{5} .
\end{array}\right.
$$ 
Then, 
$$
\left\{\begin{array}{l}
a=\frac{k}{10}, \\
b=-\frac{3 k}{10}
\end{array}\right.
$$.
Solving, we get $b=-3 a$.
Therefore, $3 a+b=0$.