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

Two-Variable Equations

College Algebra

2. Graphs of Equations

Two-Variable Equations

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1:43 minutes

Problem 11

Textbook Question

In Exercises 1-12, plot the given point in a rectangular coordinate system. (7/2, - 3/2)

Verified step by step guidance

Understand the problem: You are tasked with plotting the point (7/2, -3/2) on a rectangular coordinate system. The rectangular coordinate system consists of an x-axis (horizontal) and a y-axis (vertical). The point is given in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

Convert the given coordinates into a more intuitive form if necessary. Here, the coordinates are fractions: x = 7/2 and y = -3/2. You can leave them as fractions or convert them to decimals for easier plotting. For example, 7/2 = 3.5 and -3/2 = -1.5.

Locate the x-coordinate (7/2 or 3.5) on the x-axis. Start at the origin (0, 0) and move 3.5 units to the right, since the x-coordinate is positive.

Locate the y-coordinate (-3/2 or -1.5) on the y-axis. From the x-coordinate position (3.5, 0), move 1.5 units downward, since the y-coordinate is negative.

Mark the point (7/2, -3/2) or (3.5, -1.5) on the graph. Label the point clearly to indicate its coordinates.

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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. 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', corresponds to the horizontal distance from the origin, while the second number, 'y', corresponds to the vertical distance. The order of the numbers is crucial, as switching them would place the point in a different location within the coordinate system.

Plotting Points

Plotting points involves marking a specific location on a coordinate grid based on its ordered pair. To plot the point (7/2, -3/2), you first move 3.5 units to the right along the x-axis and then 1.5 units down along the y-axis. This process is fundamental in graphing functions, analyzing data, and visualizing mathematical relationships.