When the line with equation $y=-2 x+7$ is reflected across the line with equation $x=3$, the equation of the resulting line is $y=a x+b$. What is the value of $2 a+b$ ?
When the line with equation $y=-2 x+7$ is reflected across a vertical line, the sign of the slope is reversed, and so becomes 2 .

Since the new line has equation $y=a x+b$, then $a=2$.

The point on the original line that has $x$-coordinate 3 has $y$-coordinate $y=-2(3)+7=1$.

This means that the point $(3,1)$ is on the original line.

When this line is reflected across $x=3$, this point $(3,1)$ must also be on the reflected line.

Substituting into $y=2 x+b$ gives $1=2(3)+b$ and so $b=-5$.

This means that $2 a+b=2(2)+(-5)=-1$.