# How do you decide whether the graphs of the two equations are parallel lines: y=6x-7, y=3+6x?

$y = m x + b$ where $m =$ slope and $b =$ y intercept.
$y = 6 x - 7$ is in this form with $m = 6$
$y = 3 + 6 x$ can be rewritten as $y = 6 x + 3$. This equation also has a slope $m = 6$.
Parallel lines have equal slopes $\implies$ these lines are parallel.