Answer
a) Neither opposite reciprocals nor perpendicular.
b) Parallel
Work Step by Step
a) Find the slope of each line by writing their equation in slope-intercept form:
$4x-3y=9$
$3y=4x-9$
$y=\frac{4}{3}x-3$
The slope of the graph of $y=\frac{4}{3}x-3$ is $\frac{4}{3}$
The slope of the graph of $y=\frac{3}{4}x+7$ is $\frac{3}{4}$
The slopes are not the same, so the lines cannot be parallel. Multiply the slopes: $\frac{4}{3}\times\frac{3}{4}=1$.
The slopes are neither opposite reciprocals nor perpendicular.
b) Find the slope of each line by writing their equation in slope-intercept form.
$6y=-x+6$
$y=\frac{-1}{6}x+1$
The slope of the graph of $y=\frac{-1}{6}x+1$ is $\frac{-1}{6}$
The slope of the graph of $y=-\frac{1}{6}x+6$ is $\frac{-1}{6}$
The slopes are the same, so the lines will be parallel.