Answer
The lines have the same slopes so they are parallel.
Work Step by Step
RECALL:
$\\\\$(i) The slope-intercept form of a linear equation is y=mx+b where m = slope and b = y-intercept.
$\\\\$(ii) Parallel lines have equal or the same slopes.
$\\\\$(iii) Perpendicular lines have slopes whose product is negative (negative reciprocals of each other).
$\\\\\\$Write each of the given equations in slope-intercept form to have:
$\\\\3x + 7y=4 \longrightarrow y=\frac{-3}{7}x+\frac{4}{7}
\\\\6x+14y=7 \longrightarrow y=\frac{-3}{7}x+\frac{1}{2}$
$\\\\\\$The two equations have the same slope but different y-intercepts so they are parallel.