Final answer:
Equations II and III both have the same slope of -5/7, which means these two lines are parallel. Hence, the two parallel lines are II and III, making the correct answer (c) II and III.
Step-by-step explanation:
To determine which two lines are parallel, we need to consider the slopes of each line. In slope-intercept form, y = mx + b, the coefficient m represents the slope. We can convert the given equations into slope-intercept form to identify their slopes.
- For equation I, 5y = 4x - 5, we divide by 5 to get y = (4/5)x - 1. The slope here is 4/5.
- For equation II, 7y = 3 - 5x, we can rearrange it to 7y = -5x + 3 and then divide by 7 to yield y = -(5/7)x + 3/7. The slope for this line is -5/7.
- For equation III, 7y + 5x = -1, we rearrange to get 7y = -5x - 1 and then divide by 7, resulting in y = -(5/7)x - 1/7. The slope is again -5/7.
Lines with the same slopes are parallel. Therefore, equation II and III have the same slope of -5/7 and are parallel to each other. The correct answer is c) II and III.