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Chapter 0: Problem 6

Graph the following equations. $$ y=0 $$

Short Answer

Expert verified
Draw a horizontal line through y = 0.

Step by step solution

01

Understand the equation

The given equation is a simple, linear equation in the form of y = 0
02

Establish the type of graph

This equation represents a horizontal line. A horizontal line equation is one where y is equal to a constant.
03

Determine the y-coordinate

From the equation y = 0, it is clear that the y-coordinate is always 0 regardless of the x-coordinate.
04

Draw the horizontal line

To graph this, draw a straight horizontal line passing through the point (y = 0) on the y-axis.

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Key Concepts

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

Horizontal Line Equation
A horizontal line is a straight line that runs left to right. Each point on this line has the same y-coordinate. The general equation for a horizontal line is given by: y = c Here, 'c' is a constant. For example, the equation y = 0 is a horizontal line where every point on this line has a y-coordinate of 0. It does not matter what value x takes; the y-coordinate will always be 0. Horizontal lines are easy to recognize because they look flat and do not slope.
Graphing Techniques
Graphing linear equations like y = 0 is straightforward if you follow these steps: 1. **Identify the form of the equation:** Determine whether it is a horizontal or vertical line, or a general linear equation. 2. **Determine the y-coordinate:** For horizontal lines, this is constant. 3. **Plot the points:** Since y = 0, every x-value will map to y = 0. 4. **Draw the line:** Connect the points to form a straight line. Ensure the line extends infinitely in both directions. With these simple steps, you can graph any horizontal line with ease.
Y-Coordinate
The y-coordinate is a key part of any graph. It tells us how far up or down a point is on the graph. When graphing a horizontal line like y = 0: - The y-coordinate remains consistent. - The y-coordinate is 0 across the entire line. - The x-coordinate can be any value. In other words, points on the graph of y = 0 look like: (x, 0)where x can be any number. This makes the y-coordinate easy to pinpoint and use in graphing this type of equation.

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