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Chapter 4: Problem 54

Is the point (0,8) on the \(x\) -axis or \(y\) -axis? How do you know? \(\quad\) you know?

Short Answer

Expert verified
The point (0, 8) is on the y-axis because its x-coordinate is 0.

Step by step solution

01

Identify Coordinates

The given point is (0, 8). This means the x-coordinate is 0 and the y-coordinate is 8.
02

Understand the Axes

A point lies on the y-axis if its x-coordinate is 0. Similarly, a point lies on the x-axis if its y-coordinate is 0.
03

Compare Coordinates

Compare the coordinates of the given point (0, 8) with the conditions for being on the x-axis or y-axis. Since the x-coordinate is 0, the point is on the y-axis.
04

Conclusion

From the coordinates of the point and the conditions for points on x-axis and y-axis, (0, 8) lies on the y-axis.

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Key Concepts

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

The x-axis
In the coordinate plane, the x-axis is the horizontal line that runs left to right. This axis represents all possible values of the x-coordinate. Points on the x-axis have their y-coordinate equal to zero. For instance, the point (3, 0) lies on the x-axis because the y-coordinate is zero. Understanding the x-axis is essential for identifying where points lie in a coordinate system.
The y-axis
The y-axis is the vertical line on the coordinate plane that runs up and down. This axis contains all possible values of the y-coordinate. Points on the y-axis have their x-coordinate equal to zero. For example, the point (0, 5) lies on the y-axis because the x-coordinate is zero. In the exercise, the point (0, 8) has an x-coordinate of 0, which confirms it lies on the y-axis.
Coordinates
Coordinates are a pair of numbers (x, y) that define the position of a point on the coordinate plane. The first number is the x-coordinate, which tells you how far left or right the point is from the origin (0,0). The second number is the y-coordinate, which tells you how far up or down the point is from the origin.

To determine the location of a point, always check both coordinates:
  • If the x-coordinate is 0, the point is on the y-axis.
  • If the y-coordinate is 0, the point is on the x-axis.
  • If neither coordinate is 0, the point is somewhere else on the plane.
In summary, the coordinates of a point help you understand its exact position on a two-dimensional plane.

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Most popular questions from this chapter

Find the equation of a line containing the given points. Write the equation in slope-intercept form. (2,7) and (3,8)

Determine whether each ordered pair is a solution to the inequality \(y>x-1:\) (a) (0,1) (b) (-4,-1) (c) (4,2) (d) (3,0) (e) (-2,-3)

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form. line \(2 x+3 y=6\), point (0,5)

Graph the linear inequality \(x>-2\)

In the following exercises, graph each pair of equations in the same rectangular coordinate system. \(y=5 x\) and \(y=5\)
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