To determine the relationship between segments [tex]\(AB\)[/tex] and [tex]\(CD\)[/tex], we need to find the slopes of the lines on which these segments lie.
First, let's calculate the slope of the line [tex]\(6x + 3y = 9\)[/tex].
1. Rewrite the line in the slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope.
[tex]\[
6x + 3y = 9 \implies 3y = -6x + 9 \implies y = -2x + 3
\][/tex]
The slope [tex]\(m_1\)[/tex] for this line is [tex]\(-2\)[/tex].
Next, let's calculate the slope of the line [tex]\(4x + 2y = 8\)[/tex].
2. Again, we rewrite this line in the slope-intercept form.
[tex]\[
4x + 2y = 8 \implies 2y = -4x + 8 \implies y = -2x + 4
\][/tex]
The slope [tex]\(m_2\)[/tex] for this line is also [tex]\(-2\)[/tex].
Since both lines have the same slope, we can conclude that the segments [tex]\(AB\)[/tex] and [tex]\(CD\)[/tex] are parallel.
Therefore, the correct statement is:
- They are parallel because they have the same slope of [tex]\(-2\)[/tex].
