Answer:
The two lines are neither perpendicular nor parallel to each other.
Step-by-step explanation:
Comparing the slopes of two lines is a great way for telling whether they are perpendicular or parallel to each other.
To find the slope of the lines, start by rewriting their equations in the slope-intercept form:
[tex]y = mx + b[/tex],
where
The first line is already in this form. Its slope (the number in front of [tex]x[/tex]) is equal to [tex]3[/tex].
Subtract [tex]12x[/tex] from both sides of the equation of the second line:
[tex]4y = -12x + 8[/tex].
Divide both sides by four:
[tex]y = -3x + 2[/tex].
The slope of this line will be equal to [tex](-3)[/tex].
Two lines are parallel if their slopes are the same. They are perpendicular to each other if the product of their slope is equal to [tex](-1)[/tex] (i.e. the two slopes are inverse reciprocal of one another.) Neither is the case for these two lines. In conclusion, these two lines are neither parallel nor perpendicular to each other.
