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

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1:17 minutes

Problem 12

Textbook Question

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 5/2, 3/2)

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 given point: The point is (-5/2, 3/2), where -5/2 is the x-coordinate and 3/2 is the y-coordinate.

Interpret the x-coordinate (-5/2): Since it is negative, move 5/2 units to the left of the origin along the x-axis.

Interpret the y-coordinate (3/2): Since it is positive, move 3/2 units up from the x-axis at the position determined in the previous step.

Plot the point: Mark the location where the movements from the x-coordinate and y-coordinate intersect. This is the point (-5/2, 3/2) on 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' represents the horizontal position and 'y' represents the vertical position. Understanding this system is essential for accurately plotting points and visualizing relationships between them.

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', indicates the position along the x-axis, while the second number, 'y', indicates the position along the y-axis. For example, the point (-5/2, 3/2) means to move left 2.5 units on the x-axis and up 1.5 units on the y-axis, which is crucial for accurate plotting.

Plotting Points

Plotting points involves marking a specific location on a coordinate grid based on its ordered pair. To plot the point (-5/2, 3/2), one would start at the origin (0, 0), move left to -2.5 on the x-axis, and then move up to 1.5 on the y-axis. This process is fundamental in graphing functions, analyzing data, and visualizing mathematical relationships.