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Marco is trying to determine whether the following two lines are parallel. y = }I - 5 Which statement correctly describes the a...Asked by The
Marco is trying to determine whether the following two lines are parallel. y=2/3x+7 y=2/3x−5 Which statement correctly describes the approach Marco should take based on the best reasoning? Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts. Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes
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GPT-4o mini
To determine whether two lines are parallel, Marco should focus on their slopes. Parallel lines have the same slope but different y-intercepts.
In this case, both lines are given in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept.
The two lines are:
1. \( y = \frac{2}{3}x + 7 \) (slope = \( \frac{2}{3} \), y-intercept = 7)
2. \( y = \frac{2}{3}x - 5 \) (slope = \( \frac{2}{3} \), y-intercept = -5)
Since both lines have the same slope of \( \frac{2}{3} \) but different y-intercepts (7 and -5), they are indeed parallel.
Thus, the correct approach Marco should take is described by Statement #1: "Marco says he should verify that the lines have the same slope but different y-intercepts."
In this case, both lines are given in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept.
The two lines are:
1. \( y = \frac{2}{3}x + 7 \) (slope = \( \frac{2}{3} \), y-intercept = 7)
2. \( y = \frac{2}{3}x - 5 \) (slope = \( \frac{2}{3} \), y-intercept = -5)
Since both lines have the same slope of \( \frac{2}{3} \) but different y-intercepts (7 and -5), they are indeed parallel.
Thus, the correct approach Marco should take is described by Statement #1: "Marco says he should verify that the lines have the same slope but different y-intercepts."
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