Which statement about the following equations is correct? y=x-6, y=-x-2

Question

A. The equations are dependent because the lines do not intersect.


B. The equations are independent because the equations represent parallel lines.


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


D. The equations are dependent because the lines are the same line.

Answer 1

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

1. First equation: \( y = x - 6 \)

   • This is in slope-intercept form \( y = mx + b \) where \( m = 1 \) (the slope) and \( b = -6 \) (the y-intercept).

2. Second equation: \( y = -x - 2 \)

   • Here, the slope \( m = -1 \) and the y-intercept \( b = -2 \).

Next, we observe the slopes:

• The slope of the first line is \( 1 \).
• The slope of the second line is \( -1 \).

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

Based on this analysis, the correct statement is:

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