#### Answer

$\frac{7}{6}$

#### Work Step by Step

Solve for $y$ to obtain:
$6x+7y=9
\\6x+7y-6x=9-6x
\\7y=-6x+9
\\\frac{7y}{7}=\frac{-6x+7}{9}
\\y=-\frac{6}{7}x + \frac{7}{9}$
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
(2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Thus, the equation $y=-\frac{6}{7}x+\frac{7}{9}$ has a slope of $-\frac{6}{7}$.
This means that the slope of the line perpendicular to it is the negative reciprocal of $-\frac{6}{7}$, which is $\dfrac{7}{6}$.
Therefore, the missing expression in the given statement is:
$\frac{7}{6}$