Question

Which two lines are parallel?

I. Sy = 2x - 5
II. 5y = 4 + 3x
II. Sy - 3x = -1
A) II and III
B) I and III
C) I and II
D) No two of the lines are parallel.

Answer 1

Lines I and III are parallel.

Step-by-step explanation:

Lines I and II are parallel.

To determine if two lines are parallel, we need to compare their slopes. If the slopes are equal, the lines are parallel.

The equation of line I can be rewritten as y = 2x - 5, which has a slope of 2. The equation of line II can be rewritten as 5y = 4 + 3x, which simplifies to y = (4 + 3x)/5. The slope of line II is 3/5.

Since the slopes of line I and line II are different, they are not parallel. However, the equation of line III, Sy - 3x = -1, can be rearranged as y = 3x - 1, which has a slope of 3. Therefore, lines I and III are parallel.