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

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

Previous problemNext problem

1:10 minutes

Problem 3

Textbook Question

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 2, 3)

Verified step by step guidance

Understand the rectangular coordinate system: It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0, 0). Points are represented as ordered pairs (x, y).

Identify the coordinates of the given point: The point (-2, 3) has an x-coordinate of -2 and a y-coordinate of 3.

Locate the x-coordinate: Start at the origin (0, 0) and move 2 units to the left along the x-axis because the x-coordinate is -2.

Locate the y-coordinate: From the position at x = -2, move 3 units up along the y-axis because the y-coordinate is 3.

Mark the point: Place a dot at the location where x = -2 and y = 3. This is the graphical representation of the point (-2, 3) in the rectangular coordinate system.

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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' indicates the horizontal position and 'y' indicates the vertical position. This system allows for the precise location of points in a two-dimensional space.

Plotting Points

Plotting points involves marking a specific location on the coordinate plane based on its coordinates. For the point (-2, 3), the x-coordinate is -2, which means you move 2 units left from the origin along the x-axis, and the y-coordinate is 3, indicating you move 3 units up along the y-axis. The intersection of these movements gives the exact location of the point.

Ordered Pairs

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y). The first number, 'x', corresponds to the horizontal position, while the second number, 'y', corresponds to the vertical position. The order of the numbers is crucial, as switching them would represent a different point in the coordinate plane.