## Precalculus (6th Edition)

$\frac{7}{6}$
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: $\frac{7}{6}$