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Chapter 3: Problem 4

On which axis does the point (2,0) lie?

Short Answer

Expert verified
The point (2,0) lies on the x-axis.

Step by step solution

01

Identify the coordinates of the point

The coordinates of the point given are (2,0). The first number represents the x-coordinate and the second number represents the y-coordinate. So, this point has an x-coordinate of 2 and a y-coordinate of 0.
02

Determine the axis on which the point lies

The y-coordinate of the point is zero. Recall that for a point to lie on the x-axis, its y-coordinate must be zero which applies here. Thus, this point lies on the x-axis.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the X-axis
In a coordinate system, the x-axis is a horizontal line that extends infinitely in both directions to the left and right. It's an important part of graphing and helps us determine the position of points. When you look at any graph, the x-axis is usually the line where all points have a y-coordinate of zero.

By understanding the x-axis:
  • It helps in locating points that are perfectly horizontal from the origin.
  • It separates the plane into the upper and lower halves.
  • This axis is essential for understanding relationships between numbers in horizontal placement.
Delving into the Y-coordinate
A y-coordinate indicates a point's vertical position in a coordinate system. In the ordered pair (x, y), the y-coordinate is always the second number. For example, in the point (2,0), the y-coordinate is 0. This tells us how far up or down the point is from the x-axis. When a y-coordinate is zero, the point lies directly on the x-axis.
  • Positive y-coordinates move the point above the x-axis.
  • Negative y-coordinates move the point below the x-axis.
  • Zero as a y-coordinate means the point is on the x-axis, showing no vertical shift.
Exploring the X-coordinate
The x-coordinate represents the horizontal position of a point in the coordinate system. It is always the first number in an ordered pair (x, y). For instance, in the point (2,0), the x-coordinate is 2. This suggests that the point is 2 units to the right of the y-axis.
  • Positive x-coordinates position points to the right of the y-axis.
  • Negative x-coordinates position points to the left of the y-axis.
  • An x-coordinate of zero places the point directly on the y-axis.
Understanding the x-coordinate is crucial for navigating a plane horizontally.
Mastering Graphing Points
Graphing points involves plotting ordered pairs (x, y) on a coordinate system. This helps in visualizing and understanding the relationship between two sets of numbers. For instance, the point (2,0) shows where the x-coordinate is 2, and the y-coordinate is 0, placing it directly on the x-axis.
To graph points effectively:
  • Start from the origin (0,0), where the x-axis and y-axis intersect.
  • Move horizontally to the right or left according to the x-coordinate.
  • Then move vertically up or down based on the y-coordinate.
  • Mark the point where you stop moving.
This simple process allows us to translate mathematical data into a visual format that鈥檚 easy to read and analyze.

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Most popular questions from this chapter

Express each inverse variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 2. (OBJECTIVE 2) varies inversely with \(x .\) If \(y=6\) when \(x=2,\) find \(y\) when \(x=4\).

Express each variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. \(s\) varies directly with \(t^{2} .\) If \(s=20\) when \(t=5,\) find \(s\) when \(t=15\).

Express each combined variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 4. (OBJECTIVE 4) \(y\) varies directly with \(x\) and inversely with \(z .\) If \(y=1\) when \(x=3\) and \(z=7,\) find \(y\) when \(x=8\) and \(z=10\).

Express each sentence as a formula. The distance \(d\) a car can travel while moving at a constant speed varies directly with \(n\), the number of gallons of gasoline it consumes.

Express each combined variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 4. (OBJECTIVE 4) \(y\) varies directly with the square of \(x\) and inversely with \(z\). If \(y=1\) when \(x=2\) and \(z=10\), find \(y\) when \(x=4\) and \(z=5\).
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