Question

What is the relationship between the two equations below? y - 3x = 2 and x + 3y = -9.

A) The two equations are parallel lines.
B) The two equations are perpendicular lines.
C) The two equations represent the same line.
D) The two equations do not have a relationship.

Answer 1

The two equations y - 3x = 2 and x + 3y = -9 do not have a relationship.

Step-by-step explanation:

The relationship between the equations y - 3x = 2 and x + 3y = -9 can be determined by comparing their slopes. Let's rearrange both equations to the slope-intercept form y = mx + b where m represents the slope:

1. y - 3x = 2 becomes y = 3x + 2 (slope: 3)
2. x + 3y = -9 becomes y = -1/3x - 3 (slope: -1/3)

Since the slopes of the two equations are different (3 and -1/3), we can conclude that the two lines represented by these equations are not parallel or perpendicular. Therefore, the correct answer is D) The two equations do not have a relationship.