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Chapter 0: Problem 6

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

Short Answer

Expert verified
The graph is a horizontal line through y=0.

Step by step solution

01

Identify the Equation Type

The equation given is a linear equation in the form of y = c, where c is a constant. Specifically, this equation is y = 0.
02

Understand the Graph of y = 0

The equation y = 0 represents a horizontal line where every point on the line has a y-coordinate of 0.
03

Plot Points on the Coordinate Plane

Choose several x-coordinates (e.g., -2, -1, 0, 1, 2) and plot the corresponding points (e.g., (-2, 0), (-1, 0), (0, 0), (1, 0), (2, 0)).
04

Draw the Graph

Draw a straight horizontal line through the plotted points. This line covers all x-values and remains at y=0.

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Key Concepts

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

Horizontal Line
Let's start by understanding what a horizontal line is. A horizontal line runs from left to right across the coordinate plane. It has the same y-coordinate for all points along the line. In the case of the equation given in the exercise, y = 0, the line is horizontal because the y-coordinate remains constant no matter what the x-coordinate is.

To graph a horizontal line like y = 0, you simply plot several points where y is 0. For example, points like (-2, 0), (0, 0), and (2, 0) all lie on the horizontal line y = 0.

Once you plot these points, draw a straight line through them. This forms a horizontal line at y = 0. It's that simple!
Coordinate Plane
Next, let's take a look at the coordinate plane. This is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). These axes intersect at a point called the origin, which has coordinates (0, 0).

When graphing equations, you use the coordinate plane to plot points and draw lines. Each point on the coordinate plane is defined by an x-coordinate and a y-coordinate, written as (x, y).
If you need to graph the equation y = 0, you would place your points on the coordinate plane where the y-coordinate is 0. For example, plotting points like (-2, 0) or (2, 0) involves moving left or right along the x-axis while staying on the line y = 0.
Y-Coordinate
Finally, let's focus on the y-coordinate. The y-coordinate is the second number in an ordered pair (x, y) and indicates how far up or down a point is from the x-axis.

In the equation y = 0, the y-coordinate is always 0. This means that every point on this line will have zero height above or below the x-axis. When you graph this equation, you will see a horizontal line that cuts precisely along the x-axis.

Knowing how to interpret and plot the y-coordinate is crucial for correctly graphing linear equations. This helps you ensure that your graph accurately represents the given equation.

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Most popular questions from this chapter

Convert the numbers from graphing calculator form to standard form (that is, without E). $$8.23 E-6$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$x^{5} \cdot\left(\frac{y^{2}}{x}\right)^{3}$$

Let \(f(x)=\frac{x}{x-1}\) and graph the function \(f(f(x))\) in the window \([-15,15]\) by \([-10,10] .\) Trace to examine the coordinates of several points on the graph and then determine the formula for \(f(f(x)).\)

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\frac{1}{x^{-3}}$$

Evaluate \(f(4)\). $$f(x)=x^{1 / 2}$$
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