Final answer:
The equations y = -1/4x - 16 and 100y + 25x = 600 have the same slope, making them parallel lines.
Step-by-step explanation:
The equations y = -1/4x - 16 and 100y + 25x = 600 have the same slope, which means they are parallel lines. Parallel lines have the same slope but different y-intercepts. The first equation is in slope-intercept form, y = mx + b, where m is the slope (-1/4) and b is the y-intercept (-16).
The second equation can be rearranged to slope-intercept form by solving for y, which gives y = -1/4x + 6. Both equations have a slope of -1/4.