To determine whether two lines are parallel, you need to check their slopes. Lines are considered parallel if they have the same slope and different y-intercepts.
Looking at the given equations:
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First pair of lines:
- \( y = \frac{2}{3}x + 7 \)
- \( y = \frac{2}{3}x - 2 \)
- Both lines have the same slope of \(\frac{2}{3}\) but different y-intercepts (7 and -2). Therefore, these lines are parallel.
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Second pair of lines:
- \( y = 23x + 7 \)
- \( y = 23x - 2 \)
- Both lines have the same slope of 23 but different y-intercepts (7 and -2). Therefore, these lines are also parallel.
Given these analyses, the correct approach for Mick should be:
Statement #1: Mick says he should verify that the lines have the same slope but different y-intercepts.
This statement accurately describes the condition needed to determine that two lines are parallel. Thus, Statement #1 is the correct choice.