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Chapter 3: Problem 68

Answer each exercise with true or false. Point (3,0) lies on the \(y\) -axis.

Short Answer

Expert verified
False

Step by step solution

01

Understand the Coordinates of the Point

A point in a coordinate plane is represented as \((x, y)\). The first value \(x\) denotes how far to the right (positive) or left (negative) from the y-axis the point is, and the second value \(y\) denotes how far up (positive) or down (negative) from the x-axis the point is.
02

Definition of y-axis

The y-axis is the vertical line on a coordinate plane. Points lying on the y-axis have their x-coordinate equal to 0. This means if a point is on the y-axis, it should have the form \((0, y)\).
03

Check the x-coordinate of Point (3,0)

For the point \((3,0)\), the x-coordinate is 3. This indicates that the point is 3 units to the right of the y-axis.
04

Conclusion About Point (3,0)

Since the x-coordinate of the point is not 0, the point \((3,0)\) does not lie on the y-axis. Instead, it lies somewhere along the x-axis.

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Key Concepts

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

x-coordinate
The x-coordinate is a vital element of understanding the position of a point on a coordinate plane. It is the first number in an ordered pair \((x, y)\), denoting how far left or right a point is from the y-axis. The x-coordinate of a point tells us its horizontal position, where:
  • If the value is positive, the point is to the right of the y-axis.
  • If the value is negative, the point is to the left of the y-axis.
  • If the value is zero, the point lies exactly on the y-axis.
In our specific example, we have the point \(3, 0\). Here, the x-coordinate is 3. This means the point is positioned 3 units to the right of the y-axis, clearly indicating its horizontal placement. Recognizing and interpreting the x-coordinate is crucial in pinpointing exactly where on the plane a point is positioned horizontally.
y-coordinate
The y-coordinate in an ordered pair \(x, y\) describes how far up or down a point is from the x-axis on a coordinate plane. This coordinate defines the vertical positioning of a point, revealing whether the point is above, below, or directly on the x-axis.Consider the value of the y-coordinate:
  • A positive y-coordinate indicates the point is above the x-axis.
  • A negative y-coordinate means the point is below the x-axis.
  • A y-coordinate of zero places the point exactly on the x-axis.
In the example point \(3, 0\), the y-coordinate is 0, which means the point lies directly on the x-axis. Understanding the y-coordinate is essential for knowing a point's vertical alignment and ensures accurate graph plotting.
y-axis
The y-axis is a fundamental part of the coordinate plane, serving as the vertical datum line where horizontal and vertical positions are gauged. It is the vertical line that crosses the x-axis at the origin point \(0, 0\), slicing the plane into two halves.Characteristics of the y-axis:
  • Point coordinates with an x-coordinate of 0 lie on the y-axis, which means their ordered pair is in the form \(0, y\).
  • The y-axis helps in determining the horizontal distance of a point, which is reflected in its x-coordinate.
  • It represents all the points that do not move left or right but solely up and down.
When analyzing whether a point like \(3, 0\) lies on the y-axis, we look for an x-coordinate of 0. Since \(3, 0\) has an x-coordinate of 3, it does not lie on the y-axis, but rather on the x-axis. Grasping the role of the y-axis allows us to accurately analyze and interpret the locations of points in the plane.

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Most popular questions from this chapter

For Exercises 71 through 75, fill in each blank with "0," "positive," or "negative." For Exercises 76 and 77, fill in each blank with "x"or "y." Point \(\quad\) (_____,_____) Location \(\quad\) origin

Write an equation in standard form of the line that contains the point (4,0) and is perpendicular to the line \(y=-2 x+3\)

For Exercises 71 through 75, fill in each blank with "0," "positive," or "negative." For Exercises 76 and 77, fill in each blank with "x"or "y." Point \(\quad\) (_____,_____) Location \(\quad\) quadrant IV

Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. A Hawaiian fruit company is studying the sales of a pineapple sauce to see if this product is to be continued. At the end of its first year, profits on this product amounted to \(\$ 30,000\). At the end of the fourth year, profits were \(\$ 66,000\). A Hawaiian fruit company is studying the sales of a pineapple sauce to see if this product is to be continued. At the end of its first year, profits on this product amounted to \(\$ 30,000\). At the end of the fourth year, profits were \(\$ 66,000\).

Solve each equation for y. See Section 2.5. $$ 5 x+2 y=7 $$
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