Final answer:
The slopes of the given equations are not parallel or perpendicular.
Step-by-step explanation:
To determine whether the graphs of y = 12x + 6 and 4y = k(3x + 10) are parallel or perpendicular, we need to compare their slopes.
The general form of a straight line equation is y = mx + b, where m is the slope. The equation y = 12x + 6 can be rewritten in this form as y = 12x + 0, indicating a m value of 12. In the equation 4y = k(3x + 10), we can rewrite it as y = (3/4)x + (10/4) and see that its slope is 3/4.
Since the slope of the first equation is 12 and the slope of the second equation is 3/4, they are neither parallel nor perpendicular to each other.