Concept Check Graph the points on a coordinate system and identify the quadrant or axis for each point. (0, 5)

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Start by understanding the coordinate system: the horizontal axis is the x-axis and the vertical axis is the y-axis.

Plot the point (0, 5) by locating 0 on the x-axis and 5 on the y-axis.

Since the x-coordinate is 0, the point lies directly on the y-axis rather than inside any quadrant.

Recall that points on the y-axis have an x-coordinate of 0 and can be positive or negative along the y-axis.

Conclude that the point (0, 5) is on the positive y-axis, not in any of the four quadrants.

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주요 개념

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Coordinate Plane and Axes

The coordinate plane consists of two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical). Points are represented as (x, y), where x indicates horizontal position and y indicates vertical position. Understanding the axes helps locate points precisely.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, numbered counterclockwise starting from the upper right. Quadrant I has positive x and y values, Quadrant II has negative x and positive y, Quadrant III has negative x and y, and Quadrant IV has positive x and negative y. Identifying the quadrant helps classify point locations.

Points on the Axes

Points with either x = 0 or y = 0 lie directly on the y-axis or x-axis, respectively, rather than inside any quadrant. For example, (0, 5) lies on the y-axis above the origin. Recognizing axis points is essential for accurate graph interpretation.