To determine which of the given lines are perpendicular to the x-axis, we need to understand that a line is perpendicular to the x-axis if it is vertical. The x-axis is a horizontal line, and thus vertical lines will have an undefined slope.
Let's analyze each line:
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y = 1: This is a horizontal line that runs parallel to the x-axis. It is not perpendicular to the x-axis.
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y = x: This line has a slope of 1 (45 degrees to the horizontal), so it is not perpendicular to the x-axis.
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y = -y (which simplifies to 0 = 0): This represents all points in the Cartesian plane and is not a valid line in this context.
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The line "y = 1" is repeated. As mentioned before, it's horizontal and does not meet the criteria.
Based on this analysis, none of the lines provided (y = 1, y = x, or y = -y) are perpendicular to the x-axis. A line that is perpendicular to the x-axis would be in the form of \(x = a\), where \(a\) is a constant.
1 answer