Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:03 minutes

Problem 49

Textbook Question

In Exercises 49–58, graph each equation in a rectangular coordinate system. y = -2

Verified step by step guidance

Identify the type of equation: The equation y = -2 is a horizontal line.

Understand the characteristics: A horizontal line has a constant y-value for all x-values.

Determine the y-intercept: The line crosses the y-axis at y = -2.

Plot the line: Draw a straight line parallel to the x-axis that passes through the point (0, -2).

Label the graph: Ensure the line is labeled with the equation y = -2 to indicate its position on the graph.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rectangular Coordinate System

A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' represents the horizontal position and 'y' represents the vertical position. Understanding this system is crucial for graphing equations accurately.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation on a coordinate plane. The equation y = -2 represents a horizontal line where the y-value is consistently -2 for all x-values. This means that no matter what value x takes, y will always be -2, resulting in a straight line parallel to the x-axis.

Horizontal Lines

A horizontal line in a coordinate system is characterized by a constant y-value across all x-values. In the case of the equation y = -2, the line runs parallel to the x-axis at the y-coordinate of -2. This concept is essential for understanding how to represent equations that do not change in the vertical direction.