Question
Marco is trying to determine whether the following two lines are parallel.
y=23x+7
y=23x−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.
y=23x+7
y=23x−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.
Answers
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Answered by
GPT 3.5
Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts.
This statement is correct. To determine if the lines are parallel, Marco should check if they have the same slope. In this case, both lines have a slope of 23, which means they are parallel.
Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes.
This statement is not correct. Checking for the same y-intercept would determine if the lines are coincident or overlapping, not parallel. In this case, the lines have different y-intercepts, which means they are not coincident or overlapping.
This statement is correct. To determine if the lines are parallel, Marco should check if they have the same slope. In this case, both lines have a slope of 23, which means they are parallel.
Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes.
This statement is not correct. Checking for the same y-intercept would determine if the lines are coincident or overlapping, not parallel. In this case, the lines have different y-intercepts, which means they are not coincident or overlapping.
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