Concept Check Answer each question. If a vertical line is drawn through the point (4, 3), at what point will it intersect the x-axis?

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Recall that the x-axis is the line where the y-coordinate is zero, so any point on the x-axis has coordinates of the form \((x, 0)\).

A vertical line through the point \((4, 3)\) means the line has the equation \(x = 4\), because all points on this line share the same x-coordinate as the given point.

To find the intersection of this vertical line with the x-axis, substitute \(y = 0\) into the line equation \(x = 4\).

Since \(x = 4\) and \(y = 0\), the intersection point on the x-axis is \((4, 0)\).

Thus, the vertical line through \((4, 3)\) intersects the x-axis at the point \((4, 0)\).

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주요 개념

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Coordinate Plane and Points

The coordinate plane consists of an x-axis (horizontal) and a y-axis (vertical). Each point is represented as (x, y), where x is the horizontal position and y is the vertical position. Understanding how points are plotted helps in visualizing lines and intersections.

Vertical Lines in the Coordinate Plane

A vertical line has a constant x-value for all points on the line. Drawing a vertical line through (4, 3) means the line’s equation is x = 4, regardless of the y-value. This property is key to finding intersections with other axes.

Intersection with the x-axis

The x-axis is the line where y = 0. To find where a vertical line intersects the x-axis, set y = 0 and use the line’s equation to find the corresponding x-coordinate. This gives the intersection point on the x-axis.