Final answer:
To determine if the lines 15x-15y=-4 and -5x+5y=-3 are parallel, we need to compare their slopes. Both equations need to be in the slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept. The slopes of both lines are equal, indicating that the lines are parallel.
Step-by-step explanation:
To determine if the lines 15x-15y=-4 and -5x+5y=-3 are parallel, we need to compare their slopes. Both equations need to be in the slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept. Let's put these equations in this form.
For the first equation, 15x-15y=-4, we isolate y to get -15y=-15x-4, and then y=x+4/15.
For the second equation, -5x+5y=-3, we isolate y to get 5y=5x-3, and then y=x-3/5.
Comparing the slopes, we can see that both lines have a slope of 1. Since the slopes are equal, the lines 15x-15y=-4 and -5x+5y=-3 are parallel.