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Chapter 3: Problem 30

What is the equation of the \(x\) -axis? What is the equation of the \(y\) -axis?

Short Answer

Expert verified
The equation of the x-axis is \(y = 0\) and the equation of the y-axis is \(x = 0\).

Step by step solution

01

Identify properties of the x-axis

The x-axis is a horizontal line on the Cartesian coordinate plane. Any point on the x-axis has a y-coordinate of 0.
02

Write the equation for the x-axis

Since all points on the x-axis have a y-coordinate of 0, the equation of the x-axis is: \[ y = 0 \]
03

Identify properties of the y-axis

The y-axis is a vertical line on the Cartesian coordinate plane. Any point on the y-axis has an x-coordinate of 0.
04

Write the equation for the y-axis

Since all points on the y-axis have an x-coordinate of 0, the equation of the y-axis is: \[ x = 0 \]

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Key Concepts

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

x-axis
The x-axis is one of the two main lines that make up the Cartesian coordinate plane. It runs horizontally, from left to right. Any point on the x-axis has a special property: its y-coordinate is always zero. Imagine drawing a straight line that cuts through the middle of your graph, dividing it into top and bottom halves. This is the x-axis.
So, if you have a point like (3, 0) or (-5, 0), these points lie directly on the x-axis because their y-value is zero. This leads us to the equation of the x-axis, which is simple and straightforward: \[ y = 0 \] This equation tells us that no matter where you are along the x-axis, the y-coordinate will always be zero.
y-axis
The y-axis is the other main line in the Cartesian coordinate plane, running vertically from bottom to top.
Any point on the y-axis has an x-coordinate of zero. It divides the plane into left and right halves.
For example, points like (0, 4) or (0, -3) are on the y-axis because their x-value is zero. Drawing the y-axis is like slicing through the middle of your graph to make left and right sections. The equation to represent the y-axis is: \[ x = 0 \] This equation shows that, along the y-axis, the x-coordinate is always zero, regardless of how high or low you go.
horizontal and vertical lines
Understanding horizontal and vertical lines helps in describing the x-axis and y-axis.
Horizontal lines go left and right, parallel to the x-axis. They have the form y = constant. For example, y = 5 is a horizontal line where every y-value is 5, no matter the x-value.
Vertical lines, on the other hand, go up and down, parallel to the y-axis. Their form is x = constant. An example is x = -2, where every x-value is -2, no matter the y-value.
In summary:
  • Horizontal lines: y = constant, parallel to the x-axis.
  • Vertical lines: x = constant, parallel to the y-axis.
This understanding is crucial for graphing and solving equations in your math journey.

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