Answer
neither parallel nor perpendicular
Work Step by Step
RECALL:
(i) Two lines are parallel if they have (a) equal slopes or (b) undefined slopes.
(ii) Two lines are perpendicular if they have (a) slopes whose product is −1 or (b) if one has a zero slope and the other has an undefined slope.
(iii) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b=y-intercept.
Write both equations in slope-intercept form to have:
Equation 1:
$7x-3y=2
\\-3y=-7x+2
\\y=\dfrac{-7x+2}{-3}
\\y=\dfrac{7}{3}x-\dfrac{2}{3}$
Equation 2:
$9y+21x=1
\\9y=-21x+1
\\y=\dfrac{-21x+1}{9}
\\y=-\dfrac{7}{3}x+\dfrac{1}{9}$
The lines have unequal slopes whose product is not equal to −1.
Thus, the lines are neither parallel nor perpendicular.
