Let's analyze the given equations to determine the nature of the lines:
1. First Equation: [tex]\(6x - 2y = -2\)[/tex]
- To rewrite this in the slope-intercept form [tex]\(y = mx + b\)[/tex], we need to solve for [tex]\(y\)[/tex]:
[tex]\[
6x - 2y = -2
\][/tex]
[tex]\[
-2y = -6x - 2
\][/tex]
[tex]\[
y = 3x + 1
\][/tex]
Therefore, the slope ([tex]\(m\)[/tex]) of the first equation is [tex]\(3\)[/tex].
2. Second Equation: [tex]\(y = 3x + 12\)[/tex]
- This is already in the slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m = 3\)[/tex].
Now, we have both lines with their slopes:
- First line: [tex]\(y = 3x + 1\)[/tex] with slope [tex]\(3\)[/tex]
- Second line: [tex]\(y = 3x + 12\)[/tex] with slope [tex]\(3\)[/tex]
3. Relationship Between the Lines:
- We compare the slopes of the two lines. If two lines have the same slope and different y-intercepts, they are parallel.
- Here, both slopes are [tex]\(3\)[/tex].
Since the slopes of both lines are equal ([tex]\(3\)[/tex]), the lines are parallel.
Therefore, the correct answers for the statement are:
- The slope of their slopes is 3 (for both lines), so the lines are parallel.
