Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 6a

Chapter 2, Problem 6a

Plot the given point in a rectangular coordinate system. (- 4, - 2)

Verified step by step guidance

Step 1: Understand the rectangular coordinate system. It consists of two perpendicular axes: the horizontal axis (x-axis) and the vertical axis (y-axis). The point (-4, -2) is given in the form (x, y), where -4 is the x-coordinate and -2 is the y-coordinate.

Step 2: Identify the x-coordinate (-4). This tells you how far to move horizontally from the origin (0, 0). Since the x-coordinate is negative, move 4 units to the left along the x-axis.

Step 3: Identify the y-coordinate (-2). This tells you how far to move vertically from the x-coordinate position. Since the y-coordinate is negative, move 2 units downward from the x-coordinate position.

Step 4: Mark the point (-4, -2) on the graph. After moving 4 units left and 2 units down, place a dot at that location to represent the point.

Step 5: Label the point (-4, -2) on the graph for clarity. This ensures that the plotted point is easily identifiable.

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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', represents the horizontal distance from the origin, while the second number, 'y', represents 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.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants based on the signs of the x and y coordinates. Quadrant I contains points where both coordinates are positive, Quadrant II has negative x and positive y, Quadrant III has both negative coordinates, and Quadrant IV has positive x and negative y. Knowing the location of these quadrants helps in determining where to plot points like (-4, -2), which lies in Quadrant III.

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