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Mick is trying to determine whether the following two lines are parallel.

y = 2/3x + 7
y = 2/3x - 2
Which statement correctly describes the approach Mick should take based on the best reasoning?

Statement #1: Mick says he should verify that the lines have the same slope but different y-intercepts.

Statement #2: Mick says he should verify that the lines have the same y-intercepts but different slope

Statement # _ describes the approach Mick should take based on the best reasoning

1 answer

Statement #1 describes the approach Mick should take based on the best reasoning.

This is because in order for two lines to be parallel, they must have the same slope. The lines given in the equations are:

  1. \( y = \frac{2}{3}x + 7 \)
  2. \( y = \frac{2}{3}x - 2 \)

Both lines have a slope of \( \frac{2}{3} \). Additionally, they have different y-intercepts (7 and -2), which confirms that they are indeed parallel.

Thus, verifying that the lines have the same slope but different y-intercepts is the correct reasoning.