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Chapter 0: Problem 88

Graph each equation in the rectangular coordinate system. $$ y=-2 $$

Short Answer

Expert verified
A horizontal line at \( y = -2 \).

Step by step solution

01

Identify the Type of Equation

The given equation is in the form of an equation for a horizontal line, specifically: \( y = -2 \).
02

Determine the Characteristics of the Line

Since \( y = -2 \) represents a horizontal line, every point on this line has a y-coordinate of -2. The x-coordinate can be any real number.
03

Plot Points on the Graph

Choose a few x-values to plot. For instance, select \( x = -3, 0, 2 \). For each of these x-values, the y-value is -2. Thus, the points to plot are (-3, -2), (0, -2), and (2, -2).
04

Draw the Horizontal Line

Plot the points (-3, -2), (0, -2), and (2, -2) on the rectangular coordinate system. Connect these points with a straight, horizontal line across the graph.

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Key Concepts

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

horizontal lines
A horizontal line in a graph is a straight line that goes from left to right. These lines are characterized by having a constant y-value for all x-values.

In the equation form, it is written as: \[ y = c \ where \ c \ is a constant number \]. No matter what value x takes, y will remain constant as long as the equation stays in this form.

For example:
  • The equation \( y = -2 \) represents a horizontal line where y is always -2.
  • All points on this line will have coordinates where the y-value is -2, such as \( (-3, -2), (0, -2), (2, -2) \).

By understanding this, you can easily graph any horizontal line by just plotting several points with the same y-coordinate and connecting them straight across.
rectangular coordinate system
The rectangular coordinate system, also known as the Cartesian plane, is a two-dimensional plane defined by two perpendicular axes:
  • The horizontal axis (x-axis)
  • The vertical axis (y-axis)

Each point on this plane is defined by an ordered pair of numbers, written as (x, y). The x-coordinate describes the point's horizontal position, while the y-coordinate describes its vertical position.

For example, the point (3, 4) is 3 units to the right of the origin (0, 0) along the x-axis and 4 units up along the y-axis. It鈥檚 crucial to understand this system for graphing equations, as it provides a way to visualize algebraic relationships.
plotting points
Plotting points is the act of determining and marking points on the rectangular coordinate system. Here is a straightforward process to do so:

1. Identify the coordinates of the point. Coordinates are usually written in the form (x, y).
2. Locate the x-value on the x-axis. Move horizontally along the x-axis to this value.
3. From the x-value, move vertically to the y-value. If y is positive, move upwards; if y is negative, move downwards.
4. Mark this location with a dot.

For instance, to plot the point (2, -3):
  • Move 2 units to the right on the x-axis.
  • Then, from this point, move 3 units down because the y-coordinate is -3.

It鈥檚 as simple as that! By practicing this, you can graph any point easily and move on to more complex graphing tasks.

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