Which statement about the following equations is correct?

Question

y=x-6
y=-x-2
The equations are dependent because the lines do not intersect.
The equations are independent because the equations represent parallel lines.
The equations are independent because the lines intersect in one point.
The equations are dependent because the lines are the same line.

Answer 1

To determine the relationship between the equations \( y = x - 6 \) and \( y = -x - 2 \), we should analyze their slopes and intercepts.

1. The first equation, \( y = x - 6 \), has a slope of 1 and a y-intercept of -6.
2. The second equation, \( y = -x - 2 \), has a slope of -1 and a y-intercept of -2.

Since the slopes of the lines are different (1 and -1), the lines are not parallel and will intersect at one point.

Thus, the correct statement is:

The equations are independent because the lines intersect in one point.