Textbook Question
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
y = x²
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0. Review of College Algebra
Basics of Graphing
1:52 minutesProblem 41
Textbook Question
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?
Verified step by step guidance1
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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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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