Final answer:
The two lines represented by the equations y = 3x + 5 and 15y + 5x = -60 are perpendicular because their slopes are negative reciprocals of each other, with slopes of 3 and -1/3 respectively.
Step-by-step explanation:
To determine the relationship between the two lines represented by the equations y = 3x + 5 and 15y + 5x = -60, we first need to find the slopes of these lines. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
The first equation is already in slope-intercept form, so we can see that the slope is 3. For the second equation, we rearrange it into slope-intercept form: 15y = -5x - 60, which simplifies to y = (-5/15)x - 4, or y = (-1/3)x - 4. The slope here is -1/3.
Since the slopes of the two lines are negative reciprocals of each other (3 and -1/3), this indicates that the lines are perpendicular. Thus, the answer is b. Perpendicular.